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No. Road mechanical gear shifters are set up for the left lever to operate the front derailleur and the right lever to operate the rear derailleur.

Converting to 1X is a bit more complicated than just changing the chainset or chainring. For riding off-road, clutch derailleurs stop the chain from bouncing around & keep the chain taught. If you are converting a road bike, you will need to consider what to do with the front gear shift / brake lever. On a mountain bike with non integrated shift levers, it's easy to remove the left / front derailleur shifter. There are lots of youtube videos of 1X conversions, its a good idea to look into these before starting a 1X project.

Yes, it is more cost effective to buy a full groupset rather than individual components. Buying a groupset from Merlin allows component options too (providing stock is available), so it is also easier to get exactly what you would like.

Probably, yes. Have a close look at your current jockey wheels, if they are worn and if shifting can be vague, even with new cassette, chain and cables - then replacement jockey wheels could well be the answer. Jockey wheels spin at around 400 rpm for all the hours you spend riding, they also get taken for granted and largely forgotten about. Whilst checking jockey wheels, if your bike's rear derailleur is also well used, and not as tight as it once was, it could be more cost effective to replace the rear derailleur.

We always recommend following manufacturers instructions for fitting any component. The Youtube channels of Park Tools and GCN Tech have very indepth and comprehensive advice for completing all sorts of jobs on bikes, these are also worth watching particularly if you are inexperienced or unsure.