Filling in hearth that will be going under vinyl flooring?

Yes, a bag or two of ready mixed mortar would do the job.

2 inches will be fine to lay a sharp sand and cement mix over the top (3 sharp to 1 cement) but I would advise brushing on pva to the surface you'll be laying on to help it bond to the original surface and help prevent cracking and lifting over time.

You can get ready mixed mortar in tubs, you just add water and that’ll do the job. Wickes sell it for £5 for a 5kg tub.

Hi if you have any sharp sand and cement from other jobs that you have done around the house, then use a 3 and 1 mix, so that's 3 sand and 1 cement.

A pre mixed mortar is not a great idea if you want to lay your new floor straight away. You would need to wait around three or four weeks for the screed to dry. One option would be to get a sheet of P5 chipboard and cut it to fit. 22mm P5 would raise the level to 44mm using two pieces around 1.5 inches. If this needs raising further you could pack it up with any small pieces of chipboard. If all is well stick everything together will polyurethane adhesive. Another option is similar to your original idea but use a quality floor levelling compound. Either water based or latex based. Certain water based compounds can be used to depth of 50mm and can be walked on in 24hrs.

You would need to install a transition molding overlapping the flooring and brick. Mixed mortar would do the job also. You can buy transition molding/t-moldings which comes in all sizes, shapes, metal or wood and also used in doorways or anywhere you are using 2 types of flooring. The company that made your flooring most likely has a transition piece that is designed to end your flooring. If not you can find someting close in color from other manufacturers.