I have heard that man is pronounced 'eesh' and woman 'eesha'. I don't quite understand about the הגבר
They both mean the same, but I guess that "גבר" is used more in he "manly" (more masculine) way. For example if you want to say "He is a man", you would say: "הוא גבר" and not "הוא איש".
The other word, "איש" is more subtle and it might be more similar to the English word "person".
As boatfullogoats said, the ר is a bit like the French R in that it is pronounced further back in the throat that the English R. This can make it sound a bit like an L. If you practice listening to it a lot, you'll start to hear the difference between L, English R, and ר better.
As for ג sounding like a K, the only difference between G/K is voicing (G is voiced, meaning your vocal cords vibrate while you say it, while K is unvoiced, meaning your vocal cords are more relaxed while you say it. You can feel voicing if you but your fingers on you throat near your Adam's apple while you speak). In the context of other sounds, like vowels, which are voiced, K can sometimes sound a little bit voiced, or partly like a G--so your brain, which isn't sure whether to expect a G or a K since it doesn't know this word well yet, is picking up on the voicing around ג and subtracting it out, making the G sound more like a K. It's like when you wear yellow tinted shades and after a while things stop looking so yellow, because your brain knows things shouldn't all look yellow and it starts subtracting out the excess yellow in your vision. Again, practice listening. It may not seem like it now, but it really does get easier with time.
If your native language has a strong distinction between voiced and unvoiced consonants (such as English), they won't seem either coloured or compensated by surrounding vowels.
R in Hebrew is said so it kinda sounds like an L, kind of like French from what I've heard, it's said in the upper-back of your throat