Don't help anyone too much until a manager asks you to help. If someone is really pressing help, tell them that you are busy, but they can ask the manager to tell me to help. This way, you always get maximum credit. Every single manager that I have worked for claimed they were "different" and did not suffer from it. Usually, I give them many chances to see my value. After I am overlooked too many times, I revert to this selfish mode explained previously. In all such cases, my recognition from the manager improves. Sigh.
I don't know about that, you might want to receive some help yourself right? In some cases it might be better to work at a place that values cooperation more than competition. You sound like you would thrive better at such a work culture.
However, often leads just need something in order to know what you are doing, especially managers that don't really closely work together with their team. It can help to just mention it to your lead. Because it is easy to see what you done, but not how you have helped somebody. Just mention it in whatever recurrent meeting you have. And if helping out takes more time, I'd say it is only fair to have whoever is responsible for delivery involved in prioritization, because then it is at the detriment of whatever you are working on, which might be more important.
Often, it takes less than 15-30 minutes to help somebody get unstuck. I wouldn't enjoy working at a place where people would refuse to help me with something like that, or I would be so pressed to achieve things that I can't spare 30 minutes out of my day to help someone out.
