If you are talking about the thin cords on the fly, YES replace them. But not with bungee. I use a thin, braided, white nylon line. About 15' on both sides. A hard braid allows easy tying and untying, something the fuzzy original does not. White allows you to see it instead of stumbling over it, something which the original does not. Fifteen feet allows you to reach bushes and roots otherwise unreachable. It also provides clothesline capacity.
If it looks like rain - but hasn't committed itself yet, I sometimes do a special rig. Tie the line out flat or high, so the fly is winged up for ventilation, but loosen the line so the fly can droop to the ground or near it. Fasten a liter bottle - 2 if you expect a STRONG wind - to the junction of fly and line. Prop up the fly with a stick or paddle. If rain hits, kick out the prop and the fly will drop to protect you. If you're really lazy, tie another line around the prop and run it up to the hammock slit. Just reach down and yank the prop out.
To get into the hammock and your sleeping bag at the same time, try this. Lay the bag out on the sleeping pad in the hammock. Sit down in the entry slit, pull the bag down to your feet, insert your feet, and zip the bag up about 18"- 24". Stand up in the opening and pull the hood of the bag up onto your head, position the bag, and zip it almost all the way up. Reach back of your head and pull up all the slack in the back. Sit down and lay back, pulling your feet in. This gets you in a good position.
Most of us use a relief bottle for night time forays. Don't leave the hammock. With the bag on, stand up in the entry way, unzip, and let flicker. Again with hood on head, pull up the slack in back and lean back into the hammock.
I hang my headlight over the guy line in the top of the hammock. The gear loft is handy too.