Removing gel pot for lamp body repair

Back of lamps and an explanation of the entire lamp

So is the gel those white squiggles that look like they hold the lamp module to the enclosure? If so, I'd just scrape it off like you proposed, get both surfaces as clean as possible, then apply some adhesive to hold it together. I'm guessing something like silicone caulk (or even non-silicone, like what we have in the US called "Liquid Nails") should work fine. There are no electrical concerns that I can see; it's just bonding the lamps to the housing.

To get rid of the corrosion, try soaking the aluminum in vinegar.

I believe that white material is heatsink compound, to assist in dissipating the heat from the LEDs.
The PCB appears to screw to the housing, so an adhesive would appear to be redundant, while heat dissipation is vital with high power LEDs.

You should be able to buy the stuff in large tubes, quite cheaply, from any electronics supplier.
The white type is probably zinc oxide based, newer ones are often grey ceramic based.




To refinish the housings, I'd wire brush them then prime them with "Hammerite special metals primer".

That stuff bonds in to metals incredibly well - I once filed down some pitted metal I'd previously used it on & none of it flaked off, it filed away to nothing but stayed on the metal.

Then a coat or two of whatever colour plain or hammer finish hammerite you prefer.