All My Questions - you have been warned!

Hi Everyone

I'm new here and new to gardening really. I'm just trying a few things out this year and have a few questions if anyone has time to help?

1. My young tomato plant has lots of flowers but they've started drying up. The plant is currently in the conservatory and the temperature soars during the day, especially this week. Too hot?
2. I have planted three varieties of potatoes and two of them, Nadines and Nicolas had long white sprouts on them when I planted them. I thought that was a good thing but have read somewhere that it's not. Do you think they will still be OK as I don't want to dig them up again!!
3. Also the Nicolas had patches of white on them almost like chalk or mould... do you think they are diseased?
4. My little chilli plant seedlings were doing really well and have now started going brown and wilting. Again, too hot? How can I save them? I've tried chilli food.

I think that's all for now. Loving this weather and spying on all my neighbours from the upstairs windows to see what they're doing in their own gardens!