Hi Gary!
I've trained very briefly with FA group and joined the morning run and they do not run together. Basically walk from the gym to chatuchak park together and then run at own pace. But not everybody running. I'm now at a different gym but I live in the area so I run regularly in chatuchak park in the mornings and I see their fighters running and so far never seen a group run together but instead at their own pace. I don't think you need to be nervous about that.
Re sunscreen oh I don't think that's an issue at all. I'm super white too and I wear sunscreen too but I never felt it was an issue at all. Yes they have a rinsing station (like a shower thingy) and it's considered polite to rinse off before or after clinch (although at my gym almost none of the thais do this just maybe 1 of 10).
Best option for you is to get baht at one of the atms at the airport where you pick your bags. Follow the signs and instructions for taxi (no grab service for pick up allowed). You can also get sim cards there. Have a print out of address to hotel in thai with you for the driver. It should be around 500 baht to chatuchak area.
Re food no idea about street food but if you google restaurants+saphan kwai you will find some good options. I can recommend Cat on the roof-bar in saphan kwai for great thai food and beer.
Have a great time.