42 is the width in mm. General rule is that wider tyres are more comfy, can be run at lower pressures and give more grip especially on uneven terrain but they're usually slower than narrower tyres.
Most road (racer type) bike will be about 25-28mm, hybrids and CX bikes about 32-38 and e-bikes (plus a lot of the more extreme gravel bikes) will be around 42-48. Normally the tyre width is dependent on the rim width - if you have a really narrow rim, you can't fit really wide tyres.
622 is the rim size which (confusingly) is 700c. Vast majority of road, CX/gravel and hybrid / touring style bikes are 700c although as mentioned earlier, the rim width will vary - road bikes will have narrower rims than gravel bikes.
3.5 - 6.0 is the pressure in bar
50 - 85 is the pressure in psi
for that combination of tyre & rim. Narrower tyres, you'll need to run higher pressures, wider tyres you can run lower.
Next thing - what is causing the punctures? Is it a spoke poking through the rim bed or is it something cutting through the tyre? Usually, unless the tyre is very worn, a lot of punctures indicates something in the wheel rather than an issue with the tyre. Give it all a very careful check. Schwalbe Marathons are durable and tough but also known for weighing a lot and having a rather harsh ride quality...