Choosing a brand and gauge of strings is nothing more than trial and error. Benefits of lower gauge strings are that they have less tension and are “easier” to play on. Higher gauge strings have a thicker tone and allow you to play with lower action without fretting out.
Brand is subjective, but the same gauges of different brands can have different tensions, so try several and stick with what you like.
How often to change strings is also subjective; for me, 20 hours (about week) of playing is enough to compel me to swap them. Listen to your ear—if your guitar isn’t sparkling the way it was yesterday, just change the strings. It’s only $5-10, and if it makes you fall in love with your tone again and play all day, it’s worth it.
If your fretboard/frets are dirty then you’re going to find moving around the neck to be rather difficult. You can clean the frets with 0000 steel wool, and oil them up with lemon/mineral oil found at any musical store.
If your guitar still doesn’t feel like it once used to, you either need to get the frets formally polished, or check them for indentations and get them dressed. This essentially means shaving them down to even out the wear.
This refers to the distance of the sings to the fretboard. This can be adjusted by the screws on the bridge.
If the action is too low, strings will “fret out”, if it’s too high the guitar will be difficult to play. Remember what setting you like for future reference (usually measured in 64th’s of an inch).
Your guitars neck has an optimal amount of relief/tension that can be effected by natural climate changes. To adjust this, you need to access the truss rod. This can be reached on the headstock of the guitar. The truss rod is a rod that goes through the inside of the neck, providing counter-tension to the strings to keep it straight.
This is something that I highly suggest you take to a luthier the first time and ask questions, as you can mess up your instrument if you don’t know what you’re doing.
Don’t let silly variables get in your way—keep up on your maintenance and you’ll have a clearer idea of your capabilities.