prioritises tasks according to politics, giving 50% of a month to a project which requires 10% of the time and vice versa;
Complete their "priority" project first, in the first 10% of the time. Then either inform them that you're finished and moving on to the other project, or don't inform them and move on anyway.
Which of these you do will depend on your company culture: some are micro-managed, others have a higher level of autonomy to get on with your own workload. Your manager will find it hard to be political if you've completed the work required.
is not able to provide more staff;
Raise the issue (an email will do) in a polite, non-demanding way, so that if there are questions later over performance you can prove that you've raised the issue early in the process and you're not just being lazy and using "we need more staff" as an excuse.
Then, as mentioned in another answer, simply do as much work as you can in your own working time. You may wish to put in a little extra time, but don't attempt to do two people's work.
is not able to provide hardware;
Again, raise it early and politely. Don't demand: if you know they won't do it, there's no point in making an argument out of it or appearing difficult... just make sure it's been officially (and demonstrably) raised early in the process. Raising issues early is an important part of project management, so you're encouraging the process and covering your own back.
Again once you've done this, just get on with the work as best you can with the resources available. It's not your job to run the company. If the hardware is a complete blocker, you may have to push harder
has as standard answer "we have to do this and you are the only one who can do it";
He may or may not have a point. The simple fact is that he's your line manager, he's the one who delegates your tasks. If he asks you to do it, you should do it :)
does not want you to complain or talk to anybody else, leaving everything with him
Fairly natural - anything else undermines his position and over-complicates the management structure. Leave things with him but keep proof that you have done so (archived emails should be sufficient). Unless something is a danger to life, of course.
how should a professional behave to:
avoid being labeled as malcontent;
Don't complain in a personal way, don't push things, and don't grumble. Just get on with your work, raising issues in a tactful, neutral manner
keep things moving;
Just do as much as you can: you aren't the line manager, you aren't the project manager (presumably) - raise the issues and do a full week's work. If your line manager is aware of the issues and things still don't progress as they should, that's your manager's problem, you've performed your responsibilities properly.
avoid damaging his/her CV?
None of the above should damage your CV: you're doing your job properly. Unless you're not actually undertaking tasks that are part of your job description, then there's no reason you have to mention time frames or project delays. Your CV is about what you did, not what you didn't have time for. If you aren't undertaking suitable tasks for your job description, you may wish to consider moving jobs.