May one remove rocks from his field?
It is forbidden to do so if one’s intent is to help the areas under the rock grow. It is permitted to do so if one is removing the rock for other purposes.
May one spray pesticide on his plants and produce during Shemita?
May one remove weeds from his garden?
No. However any weed which is damaging the plant or a tree may be removed.
 This falls under the Melacha of Sikul which is Rabbinically forbidden. [Rambam 1/4]
 As this is considered Leikumeiy which is permitted.
 This falls under the Melacha of Ishun which is Rabbinically forbidden during Shemitah. [Rambam 1/4][Rambam 1/4]
 Toras Hashemitah 4/15
 This is included within the Melacha of Nekush which is Rabbinically forbidden to be done during Shemitah.