Come all who want balance. Place your thoughts. Lets do this.

I said it once, I'll say it again

 

You're missing the point here. Balance IS robotic. The most perfect balance is achieved by making everything exactly the same. But that's not fun. Therefore, the human part (aiming, weapon feel, visual feedback, VARIATION) is required in order to also make a game fun. These aren't balance suggestions, but suggestions that make the game more fun for you. Now imbalance is good in itself (see video), if applied in measured, well-argumented doses. Especially in PvP, where player experience greatly deteriorates if something is clearly better than other things



Regarding the individual weapon targets in your original post, here's why I don't agree with them.

The uac20 has 3 shots, the uac5 has 1. Naturally, the way uacs behave, this means the IS uac10 should fire two shots. Two less than the clan counterpart, minimum of 1.
A change I could understand and want to see is Clan regular Autocannons being reduced to the same amount of shells as the is uac variants, as that would fall in the trend that uacs fire more shells per pull of the trigger, and make a case for using the regular cannons which are now sorely outclassed in every way. If the IS UAC 10 turns out to be too far above the UAC baseline in terms of effectiveness, what they could do is increase the delay between the 2 shots fired per click.

Heavy Lasers are a new weapon type that trades in everything about a short duration, heat efficiency and cooldown for extreme damage. The beam itself deals more damage than other lasers in terms of DPS, as Solahma pointed out, so shortening the duration would just make laser vomit kill even faster. That's not a fun change IMO, and less duration with more damage isn't going to feel like it's a really heavy weapon (not in terms of tonnage, but power). The Heavy Lasers are well varied from the other lasers, the whole point is that they feel sluggish.
But, I would like to see consistency in pulse lasers, but instead of just 'upping the damage', i'd like to see a consistent trend of 'lower duration, equal damage, lower cooldown, higher weight', for example for pulses. The extreme range of cLPL and extremely low duration of IS LPL still sit wrong with me, and are a big part of the reason why they're often outclassing the other large lasers in most builds.

So, in the end, my thoughts on balance & fun, in a PvP video game, means that you try to make variations from the baseline, to make the game varied and fun, and give people options to choose from with weapons. But, those choices have to be fun and viable. Weapons need to follow a strict baseline of balance, tweaked as a whole with rules of variation (like amount of shells fired, cooldown, heat, any variable statistic). This, instead of being tweaked individually, so each weapon has pros and cons, and if some pros are deemed more effective than others, the rules on top of the baseline can be tweaked accordingly. This works for everything, gives people plentiful variation while avoiding power creep and imbalanced weapons. Except for a few clear outliers, such as the Gauss/PPC change where the two weapons were complimenting each others shortcomings too well (Gauss complimented high heat from PPC, PPC complimented high weight of Gauss, both serving the same long range pinpoint damage role).

Edited my post, there were some fallacies I couldn't stand behind. I edited and kept some of it and some new stuff in the spoiler ahead, but it's kinda off-topic and more on the concept of game design between PvP and PvE.

Spoiler

I feel like most of your 'balance suggestions' are technically not balance, but a suggestion to make the game more imbalanced and more fun. For you. Opinions differ, and if you don't like certain (types of) weapon, that's why you can change your mech. But you can't just go around fixing random stats you dislike in a PvP game. If you bring in too many imbalances, you take away from the fun aspect in the sense that people will have to pick a certain weapon to do well against others who bring that weapon. As was the case with poptart meta for example.
When you make a change for imbalance and want to pit people against each other, it has to make sense within a trend. For clarity, expectation and fun. Here I'll take some examples from a pinnacle of PvP games, shooters. There are all these different weapons in FPS, some have higher fire rate, but also less accuracy. some deal more damage, but have increased reload time to compensate. Some are more customizable with underslumg grenades, but suffer a range reduction in return. If you tweak one of these values 'because I don't like the reload time on the M249' the whole thing becomes objectively more powerful than others, and many players dislike that more than they disliked the reload speed in the first place.
In PvE, you wouldn't have this problem. Warframe and PayDay 2 come to mind. These games have some weapons that are clearly taken away from the baseline, but as long as the people aren't fighting each other, the AI enemies won't feel cheated to be playing against weapons that are clearly better, the player will just see a difference in how far this weapon can be taken until it reaches its limit. But, if you go PvP, all these weapons have modified rules in order to try and balance them more.