Is it normal for the big ceramic-style bulbs to get warm after a while?

You can run them all night if your entire system is rated for the load. The main thing to check is your circuit breaker. Most standard holiday light setups draw about 2 to 2.5 amps per long strip. If you're just running a few sets, you're usally fine, but if you have a lot of them plugged into one extension cord or one circuit, you need to make sure that breaker is rated high enought to handle the total amperage. Running a system that is pulling 15 or 20 amps continuously without a properly rated circuit is the only real fire risk, so keep an eye on that. Also, many people do keep their sets running through the night, and that is fine as long as they are plugged directly into the wall and not overloaded. Regarding leaving them on overnight, most light fixtures are designed to handle continuous operation, but there are always considerations. If you are using battery-powered or low-voltage LED sets, they are generaly fine for long periods. For standard incandescent strings, the components aren't meant for perpetual use, but since the current energy efficiency in lights has changed so much, I'd be guessing your new sets are low voltage LEDs. If they are, they are built to run 24/7, provided they are rated for it. If they are older Incandescents, running them non-stop could shorten the bulb lifespan, but that is more of an efficiency concern than a safety issue.

For linking strands, the safe maximum depends entirely on the wattage of the specific bulbs you have and the gauge of the wire. You cannot just link them until the circuit trips. You need to calculate the total wattage of all the strands you plan to connect and then compare that total to the maximum wattage your specific outlet or fuse box is designed to handle. Generally, for standard residential outlets, you want to stay well below the 1800 watt mark, especially if you have other major appliances running. Most new LED sets have a far lower power draw, so you shold be able to link significantly more than a few strands before hitting your limit.

I was wondering about the physical connections, since I'm not totally sure if I'm looking at these cables correctly. My setup is a little different because alot of the lights are strung across my covered porch instead of just straight on the building itself. Since I plan on running them for most of the winter, I'm worried about the connection points where the power cord meets the main plug. Do those little connectors on the light chains tend to get hot over time when left on for many hours, or is that usually only an issue with the power source? I want to make sure I'm not damaging the actual light string itself.

I had trouble with my sets tripping years ago even when the total wattage seemed low. It wasn't the power draw itself, but the quality of the connections. I learned the hard way that the tiny wire terminals often fail before the lights do. I started using a simple crimping tool to secure the wiring where the sections meet up, and that made all the difference in making sure the joints were solid and didn't overheat over time.

It's about making sure the physical path is reliable. If the wiring isn't tight at the connectors, you're asking for heat and eventual failure, regardless of the circuit breaker. Are you planning on running these through any outdoor extension cords, or are they direct wall plugs?

I agree with the point about low voltage LEDs being built for continuous operation. I actually ran my entire porch setup for over three weeks last winter before taking them down and they didn't show a single sign of thermal failure. The biggest issue I had wasn't the power draw, though. I found that my connections started getting damp almost imediately after I installed them and needed to pull the whole run back to fix the moisture intrusion near the weatherproof caps.

I don't think calculating the total wattage and comparing it to the outlet limit is the only thing you have to worry about. While the low voltage LEDs are efficient, the actual physical integrity of the wiring matters just as much. Most people just count the watts, but if you are using flimsy extension cord power, you could trip or melt before the circuit breaker ever gets stressed. You have to look closely at the wire gauge itself, not just the total power draw.