I would like to get this rose plant I came across in front of a laundromat identified (a guess is enough) as long as the pictures match a rose plant you have good knowledge about. I would like to buy it online somewhere with that information. If it can't be identified, I feel like stealing a cutting and see if it can be duplicated in my garden. It looks that good.

Two popular deep red and very fragrant roses are Mister Lincoln and Chrysler Imperial.

Based on the fact that the flowers of this plant that have faded are pink (seen at the back of the plant), I can safely rule out Mister Lincoln. I have Chrysler Imperial but it has been in my garden less than a year only and I can't say this one is Chrysler Imperial or not for sure yet. But looks like Chrysler Imperial would not be fading to pink IMHO.

Are the pink blooms on the same plant?

Yes. It is on the same plant. This is in the Sacramento suburbs and weather has been pretty hot last few weeks at the least. And flowers probably faded quickly.
There is a smaller rose next to it but it had yellow flowers and probably not a Hybrid tea rose. Probably is about one third this one's plant size. This rose plant's flower color is probably not deep red but a color you would get when red and purple colors are mixed together. Wish I had checked out its fragrance.

Would you disagree this one resembles Twilight Zone rose plant? It could be it but I could use your opinion on it.

Twilight Zone seems to have a higher petal count and larger leaves, but maybe...

Seems way too red and not enough dark purple for Twilight Zone. Also, what Porkpal said about not enough petals for TZ. None of my CIs, MLs or TZs have ever faded to pink.

Ok. That make a lot of sense. That makes me wonder if there are two rose plants in the same container. I don't know if someone would do that on purpose unless it was for their in house fun thing. That brings up a different question. Is there a possibility that the rootstock is slowly about to take over this plant? Even then, is there a rose rootstock that looks this pretty and someone would want it more than the rose plant that it is a rootstock of?

There should be some rose flower that fades from first highlighted section to second highlighted section in this picture. Even the petal on the second highlight seems to be of the same texture as the ones on the first highlight but just faded. Let me do a close analysis on it when I am there next time including fragrance test in case I see a recent flower or bud on the plant.

You should be able to look closely at the base of the pot and see if it looks like there are two plants, unless they're crazy intertwined. I've grown >500 different roses over the past 30 years, and I've never had a red that faded so much to that color of pink. But that doesn't mean that one that does so isn't out there! Best of luck in your search!

I see two different prickle (thorn) patterns on canes that suggests that there are two different plants growing closely together like Susan has suggested. The red also seems to have larger leaflets growing with it.

Got it. I see two different prickle patterns and two different leaflets too. Assuming there are two rose plants (and that they are very much intertwined at the base), what are the other possibilities for the dark red rose flower to be from. Between Mister Lincoln and Chrysler Imperial, which one has the better chance of this one being.
About the second plant that has pink flowers, I am not really interested in knowing what that one is.

Mr Lincoln is a deeper red than Chrysler Imperial , and is probably more popular. I would vote for it.

Is the red rose deeply fragrant? If not and if it isn't a rebloomer, there's a possibility that it could be from the root stock and is Dr. Huey.

I've never seen a Dr Huey as full and lovely as that.

I have several Dr. Hueys (I actually like them in small doses), and they never have that many petals. Based on flower form, I'd guess Chrysler Imperial, but based on color, I'd say Mister Lincoln. So I lean with Porkpal on Mister Lincoln. Have you ever noticed a white stripe on any of the blooms? ML sometimes has that feature.

My vote goes for Mister Lincoln too out of those two but somehow I did not feel that flower on this new plant I came across did not resemble any rose plant's I have had and I have had a Mister Lincoln for a very long time (about 12 years). I see that as a much larger plant with canes that are much thicker than this one and mine has grown to at least 8 feet tall and is slightly taller than a climber rose plant of mine (Gertrude Jekyll). Based on that I feel this rose's mystery seems to be unsolved yet. But I believe it is much closer to be solved than when I posted here. I know Mr. Lincoln rose's fragrance. That test should conclude if it is Mister Lincoln or not. Let us wait till I have a chance to do that.

Here are couple more pictures of that rose. I took it off the plant couple of days ago in the night. I did not feel it had any fragrance then. But today I feel it could be Mister Lincoln's fragrance but somehow it is not that strong (possibly since I took it too early for a cut flower). Anyway there is a clearly visible white stripe in the center.

By taking the bloom off of the plant at night, I hope you don't mean you removed it without the owner's knowledge...