Looks good, Dean.
1) Do you want to come with me?
Note that, "me" is often omitted in colloquial speech; i.e., Do you want to come with?
2) Would you like to accompany/follow me.
Note that, "accompany" is different from "follow". The former means, go with or go along, whereas the latter means that you will guide or lead.
3) Would you mind letting me know after you have a chance to talk to them.
I'd change it to, ". . . after you've had a chance to talk to/with him."
Note that, either "to" or "with" words. "to" expresses direction towards. The implication, you'll be doing most of the talking), whereas "with" expresses togetherness. The implication, both parties with be doing an equal share of the talking.