but whenever i attack the enemy world, the enemy fleet which was currently not in the area, in very large numbers and with numerous capital ships, jumps into the gravwell and joins the fight against me.
Like anything, you need up-to-date intel to know where the enemy is at all times so you know when they will be joining a battle. There are a couple of good options you have here. One is to split your fleet into two groups (unless you're Advent, which gets a lot of benefit out of sticking together with multiple capital ships, there's nothing wrong at all with sending half your fleet with one capital ship and half your fleet with another). Find out where the enemy fleet is, and then attack the opposite side of his empire. Once his main fleet moves to deal with your first attack, launch a second attack with your secondary fleet. Any time he's about to warp in and join a battle, retreat the fleet that is fighting there back to your defenses. The AI doesn't know how to deal with this, so while it's running after one of your fleets, the other returns to attacking his flank. He'll keep running back and forth until he has no planets left.
Another option when bypassing is to focus on structures and ignore the planet. This is especially true with the AI, since they often buy far too many planet hit point upgrades. Destroying a few labs and trade ports can set them behind massively. This is best achieved with carriers loaded with bombers. Entrenchment adds anti-structure frigates, but I still think bombers are the better pick for this purpose because they're also useful in battle, whereas those anti-structure frigates won't help at all in a straight fight.
The final option is to try to rush the planet, bring down its hit points, and then colonize it quickly. Build a frigate factory and several repair bays quickly. This combination will give you the defense edge you need to hold the location. You do need to ensure culture will not be an issue, and you'll need heavy bombardment capabilities to deal with a planet quickly. If it has 4500 or more, this really isn't a viable approach unless you've got insane firepower.
The AI has a tendency to retreat when its outgunned and preserve its fighting strength. Often times this means it's digging its own grave because it's not defending the last scraps of economy it has left, ensuring its army will remain weaker. However, it does drag out the game. One thing that's always worth trying to do is to "lure" the AI fleet into a gravity well with a phase jump inhibitor, and then trying to wipe it out completely in a single attack. This will allow you to overrun his empire (don't waste time colonizing anything, you can clean up his feeble attempts to pick up the ashes afterwards with ease) without facing further resistance.
My final piece of advice is not to be afraid to fight with fewer capital ships or smaller armies. It takes time to become a good judge of fighting strength, but eventually you'll find that judgment and the confidence to launch early offensives.
and if the enemy planet is dead, do the enemy still go banzai all over your forces in that region?
in other words, will they try their hardest to get the home planet back?
No, the AI becomes remarkably timid when you start capturing its planets. This can drag things out (after all, it's sitting in the defensive and forcing you to fight it where it's strong, and then taking cheap-shots at you if you leave anything undefended), but in the long run ensures the AI's defeat.