Replacement of both or one molar
Replacement of tooth #30 and 31 is recommended as both teeth are involved in the chewing function. However if there are financial reasons, then it is best to replace #30 first as it is more important of the two teeth in your chewing ability. If you have your upper second molar however, I recommend to replace #31 in order to avoid shifting and movement of the upper molar.
Replacing A Missing Molar With A Dental Implant
This is a very good question and it should not be a problem to only replace one of the two missing molars. This is done routinely and the patient usually functions fine. If you still have the upper second molar you could see some drifting of that tooth downward if the lower second molar is not replaced. I would encourage you to see a dentist that places dental implants and have a 3d CBCT (CT Scan) taken of the area to be sure that you are a good candidate for a dental implant. After looking at your particular case they will determine if one or two implants would be the best choice. Hope this helps.
Two teeth lost, can I replace only 1 with an implant
You did not state whether the teeth above are both there or not but you should be able to function OK with only a 1st molar but if you have #2 and do not replace 31 it may result in supraeruption and loss of #2. If may make sense to do them separately.
While you will probably chew just fine with first molar bite only, keep in mind that leaving your upper second molar without an antagonist (that is, a lower second molar) will most probably lead to slow eruption (downward growth) of that tooth. If that happens, be prepared for interferences in your chewing motion and loss of that tooth as well. If this is a financial decision, consider placing the first molar now and the second molar next year before the natural tooth has time to move too much.