Hello,
1. I can't understand how HD wallets are secure. In BIP of HD wallet there are around 2000 words to choose from. Its not that many combinations to brute force. How its secure? How come noone checked them all already?
If a HD wallet seed has 12 words and there are 2048 possible words, the possibility would be 2048^12. That is a huge number if you actually multiply it out. It is impossible to try all the possibilities in a century with super computers. After that, it is also possible to generate keys in different languages. HD seeds are exteemely secure in the same way as private keys, there is far too many of them.
The computation is wrong. It is a permutation hence the formula will be n!/(n-r)!. So here it goes:
2048!/(2048-12)!
= 2048!/2036!
= 2048*2047*2046*2045*2044*2043*2042*2041*2040*2039*2038*2037
= 5.2715379713014884760003093175282e+39
Now that's a ridiculous number of possible set of numbers are there which you need to give the words in order. Hence it will take you forever to take it one by one.
So just imagine there are 12 seats and there are 2048 people considering there order (since it is some sort of password or code to unlock something). So in the first seat there will be 2048 people to possibly seat on it and to the second one there will be 2047 since the first one has settled in the first seat and so on.
Combination on the other hand is a way to count possibilities with no care for order or arrangement hence in math there is no such thing really as a combination lock but rather permutation lock (a joke that every math teacher would told to his students that actually has a point).
2. I love vanity addesses since years but lately i have more and more problem finding client, that actually accepts vanity addresses (importing private key).
Now is HD wallet era, so what wallets i can choose from except old ones like multibit classic and old electrum? What Vanity address friendly clients are there (software/mobile/online)?
For Electrum, you cannot import an address into a existing HD wallet. You have to choose a standard wallet at the start and choose "I have an existing private key".
I just heard of this vanity address and done some research on how it works and I get it now. Though I don't really know any wallets that accepts vanity addresses but I use Mycelium which is a HD wallet but I think it doesn't accepts that. I'm not sure so maybe you want to check it out?