Can you mine your own transactions yourself? If no, why not? And is it you physically/theoretically or practically cannot?

If yes, is this ever practical and does anyone do it? 
As I see it now, no matter what you are taking a fraction/subset of bitcoins entire hashing power so the difficulty of finding a nonce would take longer than 10 minutes to confirm.

As I see it, for this to be practical...
Block reward + saved fees > mining costs * time

Where saved fees are the result of not having to pay other miners fees since you are doing it yourself and time is the time it takes to find the nonce. 
note: this miner wouldnt have to be running full time
Theoretically, if you can mine blocks then you can certainly include your own transactions in the block.

Practically, you are competing with every other miner on the planet to find the next block. If you "win", you get the block reward plus you get to choose which transactions are included in your block. If somebody else wins, you get no say in the matter. Unless you have a very large mining operation, the chance of you winning is so small that it's never going to happen.

Miners who do make new blocks today (somebody has to, after all) may choose to include their own transactions in their blocks.