Excel hangs due to many formulas, is it possible to create a more efficient process?

Short but useless answer -- yes, I think this file can be made to work faster. I see a lot of common "bottlenecks" in your file. I don't know what help you will need to re-write this spreadsheet, so I will just point out the problems I see. If you need help changing any of these, let us know, and we will help you make changes.

1) There are a lot of linear VLOOKUP() functions -- =VLOOKUP(value,table,column,FALSE). Linear lookups are very slow. With this many lookups, I would do anything I could to make these binary lookups (4th argument=TRUE), which means sorting the lookup tables and editing the formulas.
2) Most if not all of those slow lookup functions contain a volatile INDIRECT() function. This defeats Excel's "smart" recalculation engine and forces all of those functions (including all of those slow linear lookups mentioned) to recalculate with every single calculate event. I would go to some lengths to get rid of all of these INDIRECTS() so that these functions are not volatile.
3) I see single cell mega-formula array functions that duplicate effort. There are often parts of these formulas that are repeated for each copy of the formula. When you have thousands of formulas repeating the same array calculations, that represents a significant amount of extra effort. I would spend some time with these array formulas and see what calculations are being repeatedly performed, and move those calculations to helper ranges. These helper ranges only need to be calculated once per calculate event rather than 1000's of times.

Those are three things that I see that are common in slow spreadsheets. I don't know what you will need help with. I have not spent a lot of time reverse engineering your spreadsheet, so I don't fully understand it, nor do I have any specific recommendations. These edits could become significant edits, too. There could be some value in focusing on specific tasks and parts of the file rather than try to work on the entire thing at once. As irritating as it is, it might even be better to start over from the beginning and structure the file completely differently (for example, it might become apparent that it will be better to design your language database as a single database in a single tab rather than having separate tabs for each language).

That's what I see. Look at your file, consider what you need the file to do, what each step of that process looks like, and then let's see about making the overall process more efficient.

wow that took ages just to load (minutes) - I almost had to stop the loading!!

I agree fully with what MrShorty says. I think your entire file would be considerably simplified if you had ALL data in 1 sheet (the recognized standard method for data collection). You would then probably eliminate all of those volatile INDIRECT functions.
Helper columns can also go a long way to keeping formulas simpler, easier to understand and edit, as well as speeding things up.. For instance, in your data sheet, you could have a helper that looks at Test B4, and only marks those records for consideration - all others will be ignored, so could also eliminate the volatile ARRAY functions

If you could share your revised file, maybe we could take another look and see if we can find some more tweaks?

Also, thanks for the rep

While it is improved, I still see the same issues as I saw in the previous version:

1) All of the lookups are still slow, linear lookups (fourth argument of VLOOKUP() is FALSE or 0 and 3rd argument of MATCH() is 0). Some of these lists look like they are sorted. In those cases, it might be as easy as replacing the 0/FALSE value with 1/TRUE. In other cases, you may still want to spend some time with the lookup column/row to get it sorted so that you can use a binary lookup.
2) Like INDIRECT(), OFFSET() is also a volatile function. You might look at replacing these OFFSET()s with INDEX() functions. INDEX() is mostly not volatile, though it may still calculate more often than needed.
3) I still see a lot of duplicated effort. For example, each copy of the functions in column C and D repeats the "which column contains the information for the language in C4" lookup. One quick suggestion would be to move this lookup into a helper cell (maybe B4). =MATCH($C$4,Languages!1:1,0) in B4 (or wherever you choose to put it). Then replace all of those MATCH() functions in C and D with a reference to this helper cell. Now Excel only needs to determine which columns to pull data from once rather than thousands of times.

Those are just examples of what I see. It looks like there is still room for improving the computation time/effort in this file.

Almost all of the lookup examples on the internet are for exact match, linear lookups like you are using. If your data are sorted (usually in ascending order), then you can use a binary search by changing the third argument of MATCH() to 1 [MATCH(lookup_value,lookup_array,1)] or by changing the 4th argument of VLOOKUP() to TRUE [VLOOKUP(lookup_value,lookup_table,return_column,TRUE)]. Of course, if your data are not sorted, then it is just a matter of sorting the lookup array before running the lookup.

Wikipedia's page about binary search algorithm: https://en.wikipedia.org/wiki/Binary_search_algorithm
An example I put together than shows how a VLOOKUP() works with the binary search option: https://www.excelforum.com/tips-and-...p-example.html