How do I finish Castle's entrance? How do I avoid the homing projectile?

All the answers on this page is acceptable, but it is important to remember that by this point in the game you ought to have enchanted your sword. While it is not necessary to do so, it does make this level reasonably easy to beat. However, each sword requires its own technique.

With the Sword of Flames, the extra damage makes it rather quick to finish off opponents. On hard mode with a level 5 sword, I found that I kill all the enemies before the asterisk can hit me. The technique here is to watch your health, drink potions when your health drops low enough. If you are teleported to the beginning, drink a potion so that the countdown timer will run out by the time you reach your next opponent.

With the Sword of Life, I found that on regular mode your life will not drop to the point where you will die. The technique is to weather it out and collect candies (though I found this method of earning money rather slow in the long run, especially when you have the GMOOH potion to get to the cow level). After some time, enemies will stop spawning altogether.

If your health isn't high enough or your sword doesn't heal enough, you can use the health potions to prolong your life, however, this can be costly your fist time around. With this said, the technique most people use is the berserk potion. 5 of them are given to you by the frog for answering his questions. The problem is to once again watch your life. Couple the berserk potion with a healing potion or a fire scroll to minimize your chances of dying.

I should also offer you this caveat, this is the level you receive the armor which will reduce the damage you take. There are only a handful of items in this game, so you don't want to miss an item. If you are in a rush to beat the level, your opponents might not drop the item. I suggest that you first tank the game with potions and teleports until you collect the armor, then try the techniques mentioned above to beat the level.

Finally, I have avoided the Sword of Summoning because I have yet to play with it. However, referencing LessPop_MoreFizz's answer, the summons from fallen enemies help to extend your life and allow you more time to heal. Using berserk potions (assuming you have not yet used them all) seems to be the easiest method to beating the level regardless of which sword you use. However, if you rush through the level, once again, you risk missing the armor. I would use the same techniques used with the sword of life with the sword of summoning. Perhaps coupling the flame scroll with the berserk potion would be the easiest method to beating this level.

So, there are a few things you can do that will make this easier:

First off, you can just brute force the level, by upgrading your sword and HP. Eventually, the timing will line up and you'll make it through. This works particularly well with a Sword of Summoning, and can make the Castle Entrance a fairly effective farming spot for additional candy.

Your second option is to try to speed through. Seven League Boots go a long way here, as do Berserk Potions if you have any left from the frog or a wish. Between those two, you should be able to outrun the teleport spell and make it to the end. You might also employ a Flame Scroll to take out a Knight a bit faster if you're worried about it catching up.

For me, it seems to work fine if I use a teleport scroll directly before the homing projectile hits me. It gets slower the longer it is on its way, so keeping it "alive" longer makes it much easier for you to run away from it. Of course you have to watch it, because if you meet the next knight directly beneath the projectile, that's either bad luck, or costs another teleport scroll.