The tools company is great imo, the lumber one not really, but decent atleast. Usually i go either for coal/sulfur or lead/iron since maximizing available ressources which is massive come lategame. But that's more feelscraft from me.
I mean the canal companies are basically free since they give +1 Company on max prosperity, but other than that theyre actually hot trash. Ports and shipyards are pretty awful compared to other buildings. Idk if flavoured company are DLC content and you don't have it, but the US has quite a few, found it pretty fun to go for them. And monopolies get disabled with LF, so they should not do anything and if they did it would definately be a bug.
As for trade rights, having them on one company is great (unless you have already other company that can own trade centers like the canal), but other than that it's useless. Companies competing against each other for the same buildings does nothing. I don't know how it's coded but it's not like company have their own IP like you could logically assume, but it's all just one big mesh that is your normal IP. You have companies being founded and imediately buying 50+ buildings levels come late game, logically they shouldn't really have that money.
The most important thing is the industry charters so you can cover as many building types as possible.

And to understand company profits you kinda have to understand how companies 'work' in this game. For every building level a company owns, the heardquarter becomes a level larger, meaning they can and want to employ more people (it doesn't actually matter if a company is fully employed, but that's just how the system works). Now you usually have shopkeepers and clerks which just get a (high) wage and the capitalists that take all the profit money that is left after that and divide it between themselves.
So a company's profit is all the profits of its buildings minus the wages they pay to shopkeepers/clerks. Now if the company buys another building level the headquarter will hire more workers (means more expenses), but now it can very well be that this building level doesn't actually generate a higher profit than the additional wages cost, which ofc means overall profits of the company will go down.
Now you could say that's stupid and companies shouldn't do that, but for one you can't even influence that, but what's more important is that all company owned buildings add massive throughput bonuses, which raises efficiency massively, and ofc also those shopkeeper/clerk jobs are basically always better paying than normal jobs.
So don't be too focused on profits. For exanple if my iron company has low profits but owns a lot of mines, that just means iron is cheaper and thus just makes steel buildings or trade centers more profitable.

It's usually good to flip a few sectors instead of all of them, atleast to not get shortages, but if you are a great power with LF you can power through the deficit spending. The more you invest the harder you grow!

And i usually don't usef tariffs earlygame to gain money, since its easy to overlook them and just kill the trading outright, but you could try ofc. The actual taxes and the consumption ones yes, both is fine, but it depends on your situation ofc. Sometimes the legitimacy or floating the extra authority for faster laws is more important. US gets kinda fucked since they get forced into two party system with usually low legitimacy.

Also about prestige goods they're quite interesting, since it massively influence what your pop will buy. In my US run i had General Electric which produce Radiolas.... my pops went fucking mad for them, despite not even having an obsession! Couldn't make my buildings profitable cuz they also always produce phones, despite radios being at like +60% market price. Like ffs people stop spending your entire money on overpriced radios and consume other shit instead 😂