Rebar, splicing, Calling the code official, what................TF. You guys are doing mosquito control with a shotgun here. First, in a tiny little footing like this, rebar is not a code requirement, a need, or anything but a waste of time and money. Dig the area out to below frost. Keep the sides of the poured area sharp and clean as possible. Get all the loose material out of the bottom. Tamp the bottom vigorously with a piece of 4x4, and use the bottom of the hole as a form. Grab 3-4 bags of sacrete concrete mix, mix up a fairly stiff mix, and dump in the hole. Take a flat shovel and use it to vigorously place the mix in position by stabbing straight down into the wet mix a few dozen times to get it settled in. Reach down and use a short block of wood as a trowel, make the top surface decently flat and level............ that's all folks. Remember there are thousands of buildings (pole barns) that sit on posts that were placed in holes bored by tractor driven augers, with the post sitting on top of a single bag of sacrete, poured into the hole DRY and tamped a bit, before placing the post.
Now for those of you that have an itchy keyboard finger here, and disagree. I have done countless hundreds of these, in an area where we get 4-5' of frost, where code inspectors look at, and measure every hole, and have done so for decades. I have yet to hear of an issue with a single one of them.
As for lifting the existing beam. It takes a 4x4, a bottle jack, and a small scrap of steel to prevent the bottle jack ram from penetrating the bottom of the 4x4. If you lack a firm base for the jack, use wood blocking, like a scrap of a floor joist, or landscape timber. Take measurements from a fixed point, before, during and after. Go slow, lift in small increments. And keep your game face on, because occasionally a beam like this will make a noise like a shotgun blast as it's being forced upward. Screaming like a little girl and running is not in your best interest. LOL. Be careful, take it slow, and it will turn out great.