The county was not created until 1846. So, there will be no records pertaining to Grimes County residents before that date.
Death records were not usually kept for rural communities prior to the State mandating such. There are methods for determining that information, though. Possibilities include tombstones, newspapers, wills, probate records, etc. Of course, all of those presume the need or desire to file those types of records. Regardless, there are no official county records for birth and death prior to about 1903.
Marriage records (actually, marriage bonds) have always been a requirement. For unions prior to 1846, you will need to check the records of the parent county, Montgomery.
The Grimes County Courthouse, in Anderson, has microfilm and microfiche copies of all of the county records. If you cannot make it to Anderson, there are regional State Libraries through which one can request copies of the microfilm and fiche records.