Not generally true; companies already attempt to charge the highest rates that the market can bear, so if they could easily just raise prices, they would've already raised them before the tax to gain more profits.

In the general case, an increase in costs will come out of some combination of: 1) increased prices passed onto consumers; 2) decreased wages at the firm; and 3) decreased profits at the firm. There's no economic law that says they'll all come out of #1, unless it's such a perfectly-competitive commodity business that everyone is charging barely above cost for their services to begin with (not the usual case in Silicon Valley).

Consider the flip side: If all cost reduction were automatically passed on directly into price cuts, there would be no incentive for companies to trim costs. But that isn't the case, of course; one reason firms aim to reduce their costs is that reducing costs while keeping prices fixed is one way to increase profits. Similarly, increased costs without the ability to raise prices can reduce profits. In both cases it depends on the surrounding market.

Either to the consumer, or to the shareholders or bondholders. But that's just viewing a company as a hollow shell.

That's just ridiculous logic, you could extend that to "no companies actually have expenses".