Hi nicole - congratulations on your eggs!
From the angle of the photo you posted of your yellow, it looks like a male, but i could be wrong. Has he got a large cloaca (behind the rear legs), the ones with large cloaca are males. The ones that are plumpish looking and smaller cloaca are females. Tho if your female/s have laid then they may look a little skinnier than usual.
Just because the black one wasn't in the vicinity of the eggs doesn't mean that it might not be the mother!
Rather than remove all the eggs; think about how many you intend raising and/or selling.
If you are six months pregnant and intend raising all the left over eggs then you may find it very tiring and time consuming once they hatch and having to make sure you have enough live food for them, constant daily waterchanges, then as they get bigger having to separate them into different containers or tubs by size and feeding twice a day (some axie babies will be stronger and therefore eat more and grow faster which will leave the little ones behind. Invariably if you don't separate the big from the small then the small ones become food for the larger ones).
I have 5 babies but my sister and I helped a friend when he had a few spawnings within a few weeks. He kept and raised 100 eggs out of about 700+; and even they were time consuming. Interesting, exciting but very time consuming. Of his 2nd batch I bought my 5 and my sister bought 5. They're 3 months old now and he has 35 hungry mouths as well as his own older axies left. Also he still is doing twice daily feeding and every 2nd day waterchanges.
So its up to you. 2-3 months down the line if most of your eggs manage to survive and grow are you prepared for the work as well as a young baby? You also have to be aware that once you have raised them you'll have to find homes for them; because we like them doesn't mean they'll be an influx of people or petshops demanding them and you may end up stuck with a few extra adults if they survive.
I would say if you are prepared for that then just lift the plants out only, leave the filtered ones, or scrape them of and leave in tank for parents to eat and place the other eggs in a oontainer/tub as Lee suggested rather than try to raise the lot.
Also, when my friend took his axie eggs out first day he used tank water from parents tank and then every waterchange he changed most of the water daily but used dechlorinated water (tapwater treated with a water conditioner/ager/dechlorinator that removes chlorine and chloramines) .
While the eggs are developing you should try and get some baby brineshrimp eggs in preparation and/or a source of daphnia/water fleas if you can find them. Babies will only eat live food. Once they hatch they eat their yolk so it will be about 2-4 days before they'll require the livefood. During that time you can set up a brineshrimp hatchery. See:
http://www.caudata.org/cc/articles/microfoods.shtml
