Your paraphrasing of this statement is backwards. The true statement is that observations are used to modify the ICs of a model run in order to improve them by "knocking" the first guess model state towards the observations. The process by which this is done is called "data assimilation." Data assimilation is as complicated as the weather model's dynamical core, and there are a lot of different approaches for it, each of which as advantanges and disadvantages. Some methods are more useful for assimilating observations representative of larger scale fields. Others work better on storm-scale fields.
Yes, if not more so. Modern day NWP forecasts are strongly dependent on the ability of a DA procedure to improve the first guess for the ICs for getting a good forecast.
Jesse provided some good sources for real-time observations. You should also look up individual state mesonets, because most states in the plains now have them (OK, KS, west TX, KS, CO, NE, IA all have state mesonets that can be displayed in real-time on their own individual websites).
The SPC mesoanalysis page shows data coming from SPC's internal "surface-OA" (sfcOA) software, which runs a simple form of data assimilation applied to recent surface obs only (i.e., does not reflect updated upper air conditions, even though there are few new ones provided each day outside of the classic 00/12 UTC rawinsondes). The background field for the sfcOA (i.e, the grid that it ingests) is a 1-hour RAP forecast, which enables the software to provide 3D atmospheric information even though there are few observations to fill the atmospheric space above the ground. The RAP has a 13-km grid spacing, which is why you see fuzzy gradients in products on the SPC page. My colleagues at ESRL/GSD have devised a much upgraded version of this idea, called 3DRTMA, similar to the existing operational RTMA. It is run in near-real time and graphics are available here:
HRRR Model Fields - Experimental. It has been proposed as a replacement for SPC's sfcOA scheme, but politics and all are slowing the process of adapting it. Don't expect this system to become official use by SPC anytime soon (although you might see SPC run their sfcOA at 3 km sometime soon). FWIW, the 3DRTMA is based on the HRRR.
To be totally honest, unless you're willing to spend a lot of time researching this stuff (which is frequently being upgraded and improved), it will probably be difficult for a non-meteorologist to understand what all is going into these products enough to understand when they might not be performing well. Unfortunately that's a fact of life in a science field like this. Just do the best you can and ask questions when they come up, and hopefully someone will be able to shed some light for you.