I am going to install LED lighting. Can I use the blue J-boxes from home depot if the LED light has been design for that? Do I need to worry about insulation?

Yes, you can use the plastic old work boxes.

The issue of insulation, is dependent on the type of fixture you want to install. If the light extends into the attic, then you have to make sure of the instructions on the light. Some lights will require a 3" clearance from any insulation others do not.

If a non contact fixture is covered with insulation, the heat build up may cause the light to flicker on and off because of the light's thermal protection.

The J boxes are only for wiring. The cans hold the light and are IC (insulation Contact) or Non IC rated. It will be on the box. What are you planning to use?

I am going to install "Carlon B618R-UPC 4-1/4" Round Box, Old Work, Cubic Inches: 18", Non-Metallic" and "Halo LED Universal Surface Mount" do I need to worry about insulation?

You need to worry about insulation if the fixture is not listed as "IC". "IC" means that the device can be covered or within 3" of insulation.

If the device is not listed as " of insulation.

If the device is not listed as " then all insulation must be at least 3" away from the device in all directions.

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do I need to worry about insulation?

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In a word, NO.

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Halo 4 in. Matte White LED Recessed Surface Disk Light with 80 CRI, 3000K-SLD405830WHR - The Home Depot

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Is a surface mount fixture that can be attached to a 4" round or hex box as per installation instructions.

It may also be mounted in IC and non-IC recessed housings also as per instructions.

One thing to note. Old work boxes are not rated for fixtures (lights/luminaires) and fans. Even though the fixture is quite light, you will not be in code mounting a luminaire to this box. For new work to be in code, the box must be directly nailed or screwed to a joist and equipped with machine thread connectors. Will the LED fall out of the ceiling using an old work box? Probably not. Is it code, No.
What I would do is to find the nearest joist, drill a hole for a fan/fixture rated pancake box centered on the joist and screw the new box to the joist and the LED to the new box. The most you would need to move the box, assuming 16"centers is 8". Be safe.