Although mastering has several components, possibly the most crucial is the very last stage of the processing chain, which should be a limiter. This is able to take your input signal and drive it so that the gain is pushed as close to 0dB as possible without crossing it - which would cause clipping or distortion. Limiters don't necessarily have the same variation in their character as something like a compressor or EQ, where you might have a preferred model because of its "feel". Instead, the job of a limiter is to squeeze your signal and reduce its dynamic range. As ever, use this function sparingly, since the dangers of over-limiting are well known.
Why would you spend weeks or months on producing a track and then master it on substandard monitoring equipment? The information you get from your speakers is what you base your mixing and mastering decisions on, so it's important that you use the best ones you can get access to. This may even mean mastering in a dedicated studio - perhaps this will cost some money but along with live tracking, it's one aspect of production that really does benefit from a professional environment.
Yes, you can master in a DAW! Just make sure to separate the mixing and mastering stages, since they are fundamentally different processes. Simply create a new project and load up your stereo mix (or stems if you are stem mastering) and apply the relevant processing using plugins or outboard gear. For a practical example of how this works in Pro Tools, one of the world's most popular DAWs, you can check out this course from expert producer Joe Albano where he gives you a complete guide to mastering in Pro Tools. https://ask.audio/academy?nleloc=course/3309/mastering-essentials
The plugs that come with your DAW can do a decent job, but now that software mastering is common practice you can use a suite like iZotope's Ozone, or one of the bundles from developers like Waves or FabFilter which provide all the tools you need for mastering including specialised stereo effects, multiband compressors and EQs and advanced audio analysis tools. Which brings us nicely to...
Getting a handle on what's going on in your masters has to go deeper than simply listening. As good as your DAW's meters are, they're not likely to have the seriously heavyweight capabilities of a specialised audio analysis suite. In this course for example, you'll learn all about iZotope's Insight - one of the best analysis suites around for mixing and mastering. https://ask.audio/academy?nleloc=course/3290/gaining-insight Be sure to check it out for a complete guide to finding out exactly what's going on inside your audio.