Please advice me of a better trustworthy exchange.
For exchange I can suggest you Binance and Kucoin, both support trading with leverage and I tested them out both before and there was no problem with them at the time.
A) Will there still be liquidation even if I have funds in the account? I mean if my position if 0.5 BTC with leverage 5x, and I have 0.5 BTC in account.
B) If I add more funds to the account, will my position still be liquidated?
If you have a position open with 0.5 btc worth(with added 5x leverage) and your account balance is 0.5 btc then you will still have a liquidation price and you can still get liquidated so there is almost no difference between using your whole account balance which is 0.5 btc without any leverage and using 0.1 btc with 5x leverage(still 0.5 btc) and so to sum it up you can not get a different liquidation price by not using your whole account balance and instead adding leverage and the profit/loss outcome from both scenarios will be the same.
As for the second question: Your position still will be liquidated but as you add more funds to your account the liquidation price will get further away from your position and your chance of liquidation will be minimized, keep in mind that to use your account balance as a back up fund for your position you have to use cross margin
But I personally don't suggest using cross margin since it will make it a bit easier for you to lose even more money that you were initially planned to trade with, better to start with whatever you have in your account and in no way add any funds to it, do not make it too complicated at first, just use your whole account balance but with only 2x leverage at first and never increase your leverage or use cross margin at all and then as you get enough experience you can increase your leverage to 3x but it's better to not use any more leverage than that in crypto unless you really don't care about your money.