you shouldn't waste your time on something like this. people shouldn't even be using web wallets in first place specially not something new that pops up out of nowhere. the only reason why some newbies still use blockchain.com is because it is very old.
Do you think that there is any open source code available for this?
blockchain.com has published a lot of its backend on github.
What programming language should it be written in?
majority of programming language work as long as you are already familiar with it.
How much should it cost?
not enough to justify the effort.