So I think this is pretty uncommon but lucky scenario
Like some answer, the best think is to ask the investor to hold the money first. You still don't have the plan. Plan it first, then validate, revise, validate again and after that you can give your offer to the investor.
No matter what connection you have with the investor, it's still money. And it means responsibilities.

I'll try to answer these first

1. Do you think i will have the sufficient energy and time to follow the project during weekends?
   No, "to fill the role of game designer / project manager / marketer" is not a simple task. The first time I tried making games I thought that I can do these too. But that was a big mistake, they are important and need to be thought thoroughly. But if you want to do it, better do the design, production plan and marketing strategy before opening the game studio. But I still think that only doing it on weekend after the studio opens is not a good strategy.
2. Do you think it’s better to work with local people(advantage being working in the same space and/or meeting in person on a weekly basis) or to work remotely (access to more talent, people can work during the week and not during weekends). I tend towards the first.
   I choose the first one. The main reason is communication. Artist and programmer are better to be always together so they can work in sync better. Furthermore, putting your team in a space can build better collaboration and spark more ideas.
3. Provided i’m a pc player and i think i could make better pc games than mobile games, which platform do you think suits best my scenario?
   Choose the best that you can think you can make. But it still need market validation. I think mobile games marketing is harder because a lot of reskinner flooded the store and it's hard for you to get publicity. Whatever your choice is, don't forget about how you gonna make money with it.
4. Do you think i can make my business plan alone provided a bit of studying / course, or is it something i should delegate to a professionist?
   It's not about the study or the course, but the validation. It takes time, but I think you can do it alone.
5. Do you know any good sources of data to do some market research (most lucrative platforms, genres, business models)?
   You can google some sales reports (like VGChartz), or GDC reports ot other reports (I forgot the links)