Would Be Sending Meaning?

"I'll be sending you" means that you will be in the process of sending, but does not specify that you complete that action; it is continuous or ongoing. For example, if you are going to send someone a single set of photos, you might say "I'll send you the photos".

Would be sent or would be send?

There is no such thing as "will be send". Passive always requires Past Participle, so look out for that. The Past Participle of "to send" is "sent".

Will soon be sent or will be sent soon?

Both are correct. It's not that you can't say "will soon send". "Will soon be sending" simply says more about your anticipation or expectation.