Illustrator to Photoshop: how can I use the vectors I just downloaded?

As others have pointed out, you should be able to just use the frames on a dark backkground on Photoshop.

As you have already guessed, the alphabet is not a font.

It might also not be a good idea to just open the file in Photoshop, because most likely the letters are too small. Stock artists make their artwork small in order to get small files and then rely on their customers to scale the artwork when they use it. So you have to open it in Illustrator and then scale it.

In order to be able to select the single letters, use the layers panel to analyze the artwork. You need to click on the triangles to open the layers and see what's inside. Hopefully the artist has made a layer for rach letter and then it's easy to select them.

Please read the documentation on how to work with the layers panel and with selection tools:

How to use layers in Illustrator

How to make selections in Illustrator

I have made a video tutorial about this kind of stock files:

The Vector Clip Art Missing Manual: Glow - YouTube

And also about selecting parts in your stock files

The Vector Clip Art Missing Manual: Selecting Objects - YouTube

Have you tried opening the file and looking through the Layers panel? There should be loads of elements.

However, it is possible that the artwork is using Graphic Styles, Effects, etc.

In that case I'd try using the Expand Artwork command. You should then be able to select and delete the things you don't want.

On the marquee sign, are you able to use your direct select tool and select the shadow to delete it?

First of all, I wouldn't say this is a naive question. We've seen variations of this question for a while from a lot from people who get vector stock images with various kinds of glows--usually on what appears to be a transparent background. Here's an example Shutterstock images and 'transparent' backgrounds. HELP PLEASE

You might try laying out your letters in Illustrator and put them on a solid dark background. Then also in Illustrator isolate which sign you want and keep it on a solid dark background. Then bring both of those separately into Photoshop to apply blend modes and masking there.

This is one of many unfortunate (IMO) examples of Illustrator artwork that ends up being a deception of sorts. All that lighting, twinkle, and flare requires use of effects that simply don't transfer or re-purpose well. There's just too much transparency interaction, and any disassembly produces an undesirable result. I suspect very few people who download this end up figuring out what to do with it. Even if you could copy/move select characters out of that glyph-set to the marquee-style signs, they won't work on the white sign background like they do on their original black backing.

The upside to your situation is that you plan to use it in Photoshop anyway, which is where stuff like this belongs (again, IMO).

In your shoes, I'd try just opening the files in Photoshop right from the beginning and cutting them up there for my purposes. Whether you'll be able to work that successfully carries no guarantees either.

Am I right and you are not having trouble to open those assets in ​Illustrator​ but simply you need a helping hand to work with Illustrator?