Purchasing US real estate as a Foreign National

[Ephraim Lett]

Good day everyone. I am new to the industry of real estate and I have been reading and educating myself on some steps and procedures of purchasing real estate in America; particularly Florida.
Being a foreign national, I realise that there is some red tape that I need to overcome; 
1) Such as creating a bank account (which I read only two banks offer to create accounts for foreign nationals and I must come to America to create it).
     1.1) I've also read that I should open a business account to pay less taxes. I'm not sure how that works though.
2) Downpayment for foreign nationals are set between 35%-40%... nothing lower!
3) Lenders only offer to purchase properties for a minimum of $150,000.

Basically I would like to know if these obstacles are accurate and if so how do I overcome them. Personally I have no problem with coming to America to open the account, however if I can do it eletronically it would be a big help.
Also, is 35%-40% the best offer available for me?
Finally, why can't I purchase a cheaper properties through lenders?

Thank you guys for your help in advance.