Re: shredded paper around tomatoes ... paper will blow away... you may want to put heavier material on top ... once paper starts to compost down, it won't blow away.

Re: free mulch from city recyle yard. Mostly would be OK, but since that material is from the 'yard-waste-bins' at each house, in addition to larger loads from tree trimmers, etc ... there is a possiblity that diseased plants disposed of by households, might be a problem. If you decide to compost the free mulch, that would be OK. and since the odds of getting diseased plants in the mulch are very small .... roll the dice. I got some japanese beetle grubs in a load of 'free' mulch, and that was a royal pain. When I see tree trimmers working in the neighborhood, I ask if they will dump their load in my driveway ... usually get a yes.... no worries with mulching with that material.

Shredded paper is very light weight and tends to get blown away by any wind, so usually it is better to plunk the paper, unshredded, down and cover it with something else to hide it and hold it in place,
The chipped wood from those trees would make a very good mulch and it matters not which species of tree the chips come from. While most all of a tree is dead freshly chipped wood from living trees can have a fairly high Nitrogen level, which is why a large pile of freshly chipped, living wood steams more often then not. There is enough of the right ratio to allow the bacteria to get to work.