(It is forbidden to receive payment for blowing Shofar on Rosh Hashanah even if one was hired before Yom Tov. If one receives payment for the blowing good fortune will never be seen from this money.) [However there are opinions which rule that it is permitted to receive payment for blowing the Shofar. Nevertheless according to all opinions one will not see good fortune from this money received.]
Havlah-Receiving a single lump sum that includes weekday work: The above prohibition is only to receive a payment that is solely for blowing on R”H. It is however permitted according to all to receive payment for blowing Shofar on R”H if the money is included in the payment [i.e. Havlah] of blowing Shofar also during the week. [Thus if the Baal Tokeia was also hired to blow Shofar during Elul he may receive a single sum that includes the payments of both jobs. Likewise if the Baal Tokeia had to prepare and practice blowing from before Yom Tov then he may receive a single lump sum as explained in the Q&A-see there! Some were even particular to pay the Baal Tokeia for his work, using the above allowances, and refused to allow him to blow for free.]
One may not receive payment for blowing Shofar on R”H although he may receive payment for practicing before R”H and this single lump sum may include also the payment for blowing on R”H.
May one hire a Baal Tokeia on Rosh Hashanah itself, in exchange for payment?
According to all on Yom Tov it is forbidden to hire someone to blow the Shofar and this leniency hence only applies if one hires the blower before Yom Tov.
May the Baal Tokeia receive payment in one lump sum [Havlah] if he also practiced during the week?
Yes. If the Baal Tokeia had to prepare and practice blowing from before Yom Tov then he may receive a single lump sum that includes the payment of all of his work, including the blowing on R”H.
May the Baal Tokeia receive payment in a single lump sum if he was also the Chazan for Selichos?
This matter requires further analysis.
May a Chazan receive payment for his Davening on R”H?
According to all if the Chazan was also hired to Daven during the week [Selichos or another important weekday Davening and the like] then he may receive a single sum that includes the payments of both jobs. Nevertheless even if the Chazan did not do so the custom is to be lenient to allow a Chazan to be paid for Davening on R”H.
 585/11 [parentheses in original]; First opinion in Admur 306/11 [see below] unlike second opinion and custom mentioned there
Background, other opinions and explanation of ruling in 306/11:
In this Halacha Admur rules that it is forbidden to receive payment for blowing Shofar being one may not receive payment for work on Shabbos or Yom Tov. This follows the opinion brought in the Tur 585 [in name of Rav Yechiel] and Mordechai and is the first opinion mentioned in 306/11 [and Michaber 306/5]. However in that chapter [Tur 585; Admur 306/11; Michaber 306/5] a second opinion is recorded. That opinion states that it is permitted to receive payment for performing Mitzvahs on Shabbos, as the Sages did not decree against receiving payment when a Mitzvah is involved. Admur there concludes that the custom is to be lenient and receive payment for performing Mitzvahs on Shabbos or Yom Tov. Nevertheless according to all good fortune will never be seen from this money being that it is payment for work performed on Shabbos, even though it was permitted for the sake of a Mitzvah. The question arises why in this chapter Admur does not record this lenient opinion and custom. Furthermore in 585/5 the Michaber does not record that it is forbidden to receive payment for blowing Shofar and rather that the money received for payment will not see good fortune. The M”A 585/12 emphasizes that according to the Michaber it is not forbidden to receive payment for blowing Shofar being that it involves a Mitzvah. [However see Tosefes Shabbos 306/12 who explains Michaber differently than M”A] Hence why does Admur here record that it is forbidden? Some answer that on Yom Tov one is only allowed to receive payment for the actual Mitzvah that is performed on Yom Tov and not for the preparation for the Mitzvah that is performed on Yom Tov. Now since the blowing of the Shofar is not the actual Mitzvah, but rather the hearing of the sound, it is therefore forbidden according to all to receive payment for the blowing itself as this is not the actual Mitzvah. Hence in this Halacha Admur does not record the lenient opinion. [Chikrei Halachos 1 p. 32] Perhaps it is for this reason that Admur recorded this ruling in parentheses as this differentiation is not brought in former Poskim. This also explains why Admur here did not record the full ruling of the Michaber in 585/5 which adds “”or to Daven or to translate the Torah” as regarding these actions the payment is for the Mitzvah itself and in these matters one is allowed to be lenient. However this matter still requires further analysis as in 306/11 it is implied from Admur that the lenient opinion is also lenient regarding receiving payment for blowing Shofar. Vetzaruch Iyun
 The reason: The reason for this is because it is forbidden to receive payment for work on Yom Tov as explained in chapter 306/8-11. [ibid] There it is explained that the reason it is forbidden to receive payment for work on Shabbos or Yom Tov is because one may come to rent on Shabbos which is forbidden due to a decree that one may come to write. [306/11]
 M”A 585/12; implication of Michaber 585/5; second opinion in Admur in 306/11 and the final custom mentioned there; Elya Raba 585/17; Beis Meir; Kaf Hachaim 585/49; See background
 The reason: The Sages did not decree against receiving payment when a Mitzvah is involved as the entire prohibition of receiving payment is because one may come to rent and that itself is due to a decree that one may come to write [hence for the need of a Mitzvah the Sages did not extend their decree]. [Admur 306/11]
 Admur 306/11; Michaber 585/5 as explained in M”A 585/12 [see background]
The reason: As nonetheless the money is payment for Shabbos despite the fact that they permitted it for the sake of a Mitzvah. [Admur ibid]
 306/11 [regarding Chazan] and 8 [regarding all cases]; See Alef Hamagen 585/24; Piskeiy Teshuvos 306/1
 Alef Hamagen 585/24
 Griz of Brisk brought in Teshuvos Vehanhagos 2/279; Piskeiy Teshuvos 585/11; See Michaber 53/22
 M”B 306/23 in name of Beis Yosef in 585, brought in Kaf Hachaim 585/49
 Aruch Hashulchan 306/12; Piskeiy Teshuvos 585/11; SSH”K 28 footnote 145
 See Piskeiy Teshuvos 206/1
 Seemingly the allowance of “Havlah-inclusion” is only if the payment is included within payment of the same type of job done during the week, such as practicing blowing or blowing in Elul, and not for a different job. Thus the Alef Hamagen 585/24 differentiates between the form of Havlah for a Baal Tokeia and Chazan, and does not mention that the Baal Tokeia can get paid with Havlah also if he was Chazan by Selichos. However seemingly this would only apply if the person is receiving two different payments, one for being Chazan and one for blowing Shofar, in which case even though he receives the two payments as one sum it does not suffice. If however he was generally hired for all of the Shuls positions for the High Holidays which include Selichos and blowing Shofar, then seemingly this is allowed as he was not hired specifically to blow Shofar or say Selichos but to fulfill the necessary positions of the Shul. Vetzaruch Iyun.
 Admur 306/11; See Ashel Avraham Butchach 306/5
 Alef Hamagen 585/24; Piskeiy Teshuvos 206/1 [that it must be a prayer that he is normally paid for]
 Admur 306/11 in his final ruling of the custom [see background]