Is there any point to start playing in a TBC server now?
Yes, it would be really useful to start your character now, you can level their professions, fill up their quest log ready for turn-in, get exhausted with stormwind/orgrimmar to reduce the cost of epic flying, and gear up a little bit to help make leveling in WotLK Classic a bit easier, etc.
I don't want to be in a server full of whales where I can't ever progress with my char because of GDKPs in the future.
I think this rhetoric is a bit overblown. GDKPs are not going to make it impossible for you to play the game. Join a server with a good population and you will find all types of guilds for all skill levels and playstyles.
So I was thinking of starting on a fresh server with a boost char. Is it possible?
Blizzard confirmed they will not allow boosts on fresh servers for at least 90 days (keep in mind they said 90 days is the minimum, they might prevent boosts for longer)
And regarding professions how hard, i.e. time consuming, will it be to level fom 1 to max? I'm thinking mining and engineering.
Mining is dependent on the server you roll on. The higher population the server, the more difficult it would be to level (especially the later levels). Engineering is relatively easy to level, although it gets a bit expensive at the higher levels.