Certainly it can't hurt to send in a resume, but with any large company, it'll get tossed in file 13 by the HR department because it doesn't "meet the template". You might have a chance if you can find a way past the HR gatekeeper to the actual person offering the job.
So make your resume fit the template. I've been hired by quite a few large companies (AOL, eBay, Bell Canada, wtc.), and haven't had any trouble getting past HR. In fact, that is the easy part .. just charm and smiles .. HR numpties have a checklist of words / acronyms that they can't pronounce and pass along candidates who nod knowingly when they are asked.
(1) You usually never get a response on resumes you send. It just vanishes into the unknown. This is the norm. If there's no response after a couple weeks, I assume that it was rejected and work accordingly (send in a different resume if I am still interested in the company or move on).
I disagree. I get calls from more than half of the resumes I send out ... about 65%, actually.
You have to target the companies that to which you are applying. Hit the companies that are actively hiring (obviously) and follow up when you can.
2) You may have headhunter type agencies offering to work to place you with companies. If they want a fee from you, walk away. The agencies will get paid by the company offering the job, not you. If they want some money from you, it's very flaky. This can be different for the executive level, but is true for the other levels.
Good advice. Headhunters are well paid by the hiring company and can be quite aggressive.