It does appear that mating could be taking place, however, when on flat surfaces, the male usually will physically mount the hen (feet on her back).....a side picture may have offered better detail.....
Yes, you can pull 4-5 feathers from their breast or back & send those in, but you need to decide who you want to do the testing & get 2 kits from them, one sample kit for each bird.....just be sure, when you pull the feathers, that you put the sample in the shipping envelope/container & complete the paperwork for one bird before you do the other......
There is a new member on the forum with a testing lab in Canada, that has good rates, so you might want to give them a try.....
When you yank the feathers, grab 4-5 next to each other...they don't have to be large feathers, but something larger than downy feathers. Grab them firmly & give them a good yank...do it right & the bird will hardly feel it. Follow the directions for sealing & sending & just sit back & wait for the results.....
While Copperarabian's pic does definitely show the beginnings of a new clutch, your second pic may also display a conjugal visit as males will sometimes grab the feathers on the back of a hen's head/neck, for better purchase/balance.....