Hello all!

I am hoping I can share my experiences of a couple of industry traps with other FTBs and have some questions answered at the same time. I apologize in advance if my questions are stupid.

Backstory:
I am a FTB and purchased my home last summer.
Being a bit naive I was sucked into a few idealogies that in pratice are a huge con, firstly I stuck my savings into the helpful-sounding 'Help-To-Buy ISA' and saved up elsewhere hoping to use this for a deposit; But I was then told after signing the paperwork for the house that it couldn't use this for the deposit and it would be applied for AFTER the house had been purchased, this left me 2k short so a quick money transfer from a credit card saved my dream from being shattered. It's fair to say that even now, 7 months on, I have no idea what happened to the so called 'bonus' from that account.
Secondly the estate agents who were selling the house had an offer on whereby you'd save yourself £1000 off the price if using their services, it sounded fantastic so I signed up figuring it would, at minimum, make the process smoother (wrong!).
In pratice all they actually did was offer the sellers £1000 off whatever price you offered, e.g. 175k became 174k and just like that they saved you £1000.
As well as this they had a 'Lifetime' mortgage broker fee, whereby for £500 you could use their mortgage services as many times as you needed to for only a £99 admin fee a time, I later found out that there are companies who actually offer the same mortgage services for free but again, I was naive, hopefully this post saves somebody from the traps.

End Result and issue:
I am now on a 95% LTV 3 year fixed rate mortgage (I only had a 5% deposit) which puts me on remortgage time around the time of Brexit, it is only natural to assume that with Brexit's uncertainty the rate is going to rise so am wondering how best to approach this.

Questions:

1. Is there a penalty for remortgaging slightly earlier to avoid any escalated 'fear prices'? Or am I simply being dramatic?
2. How exactly does Remortgaging work and how often can I remortgage?
3. Can I keep the same provider but switch to a better rate?
4. Am I locked in for another 'minimum period' or does the period left move with me?
5. What if my house has increased in value?