I can not see your images on my Safari and Chrome browsers from my Mac. However, dividing parsley in half is likely to kill the plant. Did you manage to maintain a very long intact tap root for each half? Older parsley plants have roots that penetrate very deeply in the soil.

I live in a cooler climate compared to you. However, I notice that parsley and lemon balm do best in the cooler weather of late spring and early fall in my garden. Therefore, I think you are seeing signs of heat stress. Perhaps you could water more often to maintain the health of these plants.

This photo has about everything going on in the parsley (spots, browning, yellowing, etc) I'm not sure about the roots but both seem to have new leaf growth in their centers. They are small and slow growing but since I didn't grow these from seeds, I am not sure at the rate at which they should be growing.

I can't see the photos either.

When you say you cut the parsley in half, what do you mean? You had more than one plant clumped together, and you separated them? Depending on how long ago it was, it might be just stressed. They say parsley doesn't like its roots tampered with, though I've never divided parsley beyond the seedling stage. Have you fertilised at all? You could try a seaweed solution or something; they usually purport to help with stress and slow growth.

I've had the Lemon Balm for many years... maybe 3-5? but it always gets around this size then dies off to near death, then somehow comes back to life, repeat.
I bought the parsley late Feb and split it a few weeks ago, 2-3. A few of the ends dried up during the split, but it adjusted and seemed fine for a while. Recently though it seems to have done what it is doing now. I was afraid it might be blight or over watering as I have a family member that waters all the plants if they appear dry. It's getting pretty hot around here so the top layer of soil dries pretty fast creating the illusion the plant has no water. I usually check the dirt to make sure but I don't think they do.

I have never fertilized either plants, and am not sure what to give them. I have all purpose miracle grow and we have some grass fertilizer (so basically nitrogen). I'll check out that seaweed option though! Whatever helps out the plants.

It seems that the trouble is confined to older leaves, so, personally, I wouldn't worry about those specific symptoms.

Lemon balm is a hardy perennial which can grow into a large clump and a pot is not the best environment for it. It can be cut back like any perennial in autumn or spring to allow fresh new growth to grow up. Last year's growth will always look ratty. BTW, what is the creamy coloured stuff in the pot with the LB. Is is the remains of a previous container? If so I'd get that out of there.

Parsley is biennial which means that it will die in its second year anyway. So there is little point in trying to split it. You just need to sow fresh seed every year.

Since both are grown for their leaves the Nitrogen will be fine.

Yeah you need to be trimming that lemon balm quite a bit to keep it growing and healthy. Herbs are meant to be browsed to spur on new growth. Make sure you cut above the nodes to ensure new growth. Kind of like basil.

Also in full summer I have my lemon balm in a pot that only gets morning sun and is in full shade from midday on. That keeps it green and nice.

Thanks everyone for the help! I trimmed off all the decaying parsley stems and I'll fertilize them later when the soil dries up a bit more. (the beige 'thing' in the lemon balm pot was just a leaf from the grapefruit tree our old neighbors planted between our houses. They fall everywhere, along with their fruit haha) It's going to be extremely cloudy for the next 4 or so days with chances of rain later down the week so i'll see what that does to them. I'll probably go out and trim the lemon balm later today before the rains come. Thanks again for all the help everyone.

Parsley is not a perennial, and if you try to divide it you will likely kill it. Since it is a biennial, though, it will overwinter that first year and come back in spring with the goal of making seeds. In addition to replanting the second year, let some of the second year plants go to seed, and you should have an ongoing supply of parsley year to year.