League of Legends (LoL) Question: How do i improve my gamesense

When you want to improve at a skill in League there are a few steps you could follow:

1. Identify what you want to improve
2. Set a goal
3. Execute it till it becomes a habit

In terms of map awareness there are actually a lot of things you can do:

1. Look at the minimap
2. Look at your teammates' health & mana bars
3. Moving your screen to check on your teammates (F keys/keybinds/left clicking on minimap)

Rather than trying to do everything at once, try setting one goal first. It's easier to focus on one thing rather than many. For example: 'I'm going to check my minimap every time I lasthit a minion'. Then (try to) do this for a number of games.

The question of whether fights are winnable or not is a more complex one. It depends on stuff like numbers advantage (if you join, do you make it a 2v3?). On your teams' & the enemies' health (if your team is low they're not likely to be able to help you). And on cooldowns (do your allies/enemies have summoners/abilities/ultimates up). Ultimately I think the best way to get to know this is just joining fights and then (after the fight or watch the replay) ask yourself WHY those fights were won or lost.

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you should be looking more at the minimap than the rest of the screen more (quick blindspot checks as if you were driving I guess).

just gaining awareness through experience and knowledge of not just your champion that you are playing but basics of the enemy champions as well. This will tell you if you can add value to the fight or should you get an advantage elsewhere.

Map movement, vision and objective prep all this you can surely learn from watching pro-plays but making correct decisions will only be learnt through making mistakes. Train your gut, it will get better every game.

One last point is that you should try to be average in all the lanes across the board, then be proficient in your favourite ones, then you'll know what/why/when your team is doing something and how you should react to it. logically speaking, you can easily pick-up by playing other roles to know when the other laner is/was needed.

If you want to improve your general macro, I hate to sound like a broken record, but I suppose you should just continue to play the game. Game knowledge comes from game experience after all. A previous answer already gave excellent advice on map awareness, so I'll just skip to winning fights.
When trying to determine the outcome of a potential fight, you need to consider:
1. What abilities and spells are available on both sides (namely ultimates and summoner spells)
2. Health and Mana. If your allies have low health and mana, they are at a major disadvantage against a full health enemy group.
3. Champions in the fight. Even if you coming will only make the fight a 3v3, remember that champions make the difference in the fights, not just numbers. A full Health and Mana 2v2 with a Fiddlesticks and an Irelia vs a Janna and a Talon will be more likely to go in the direction of Irelia and Fiddlesticks, as they specialize in these situations. Try to recognize that some champions can single-handedly win a teamfight if played correctly. This will be a major determining factor of the fight.