That depends on your definition of "quality". For some people a 1 carat D/FL is preferable to a 3 carat K/SI, and for others the opposite is true. Either can be found for $20k or so.
Fluorescence: visible light emitted by a diamond when hit by UV radiation. It can alter the perceived colour of the stone and in extreme cases it may alter its transparency... when sufficient UV is present in the light, which means "outside in a sunny day". It makes a stone more difficult to sell and thus generally cheaper.
Cloud: a type of inclusion that looks like a cloud: it's fuzzy, it's made of 'droplets' (technically "pinpoints") and it can vary in colour and transparency from almost transparent "white" to very dark and opaque grey and in size from a fraction of a mm to the whole stone. In extreme cases (where clouds are the only or main "grading characteristic" for clarity and the clarity grade is SI or below), clouds can make a stone look... well, cloudy. Not lively and even not transparent.
Crystal: what it says on the tin. A mineral crystal that is included in the diamond. It can be transparent (e.g. another diamond), it can be white/whitish (e.g. calcite), or it can be very dark or black (e.g. diopside). Crystals can be some of the coolest inclusions ever, but they can also be a right pain in the neck if they are dark, strongly contrasting and maybe visually reflected across the whole stone multiple times.
Knot: a crystal (see above) that breaks the surface of the stone. Normally it's another diamond, and it can be a risk factor in as much as the smaller crystal could detach and leave a hole in the diamond. In practice, given the temperatures and pressures to which a diamond is subject when it is being cut, if it had to happen, it would have happened already... but people don't like them much.
If you are talking about lab reports, GIA is certainly reliable and usable by a consumer as an honest guide to what a given diamond is like. AGI I have never heard of (which for me also means "no, it's not a reliable source of information for a diamond I intend to purchase"). If you meant AGS it's roughly on a par with GIA, but it has a much more complex and selective cut grading system, so I would also trust a lab report from AGS. Other labs are by and large more questionable in at least one aspect of their grading - it doesn't make the stones that come with those reports "bad", but it does raise question as to why the seller is marketing a given stone with second rate credentials.
Note that although the lab report is important (crucial in certain cases where presence/absence of treatment can add one, two or even three zeros to the price), it doesn't necessarily provide a buyer with everything they want or need to know. Necessary, but not sufficient, in mathematical language.
Again, it depends... three main factors:
1. What does the price include? I assume it is for a loose stone and net of sales taxes. If the price you have been quoted includes 5-10% sales tax and a plain, good quality solitaire setting then clearly we are comparing apples and pears.
2. How important are various characteristics for you? I would not buy a "VG" cut without knowing quite a bit more about it than depth and table, and I'd rather have a fantastically cut 1.80 ct. stone than an indifferently cut 2.00.
3. How important is it for you to shop on your high street/local mall vs. using a broader net including other places ("virtual" or real, just somewhere else). There are advantages to using a local store, but generally they do have higher prices than what one can find online. For example, here is a 2 carat G/VS1 XXX with medium blue fluorescence which seems to be very well cut and is a shade under $20k: https://enchanteddiamonds.com/diamonds/view/R202-278572Z43?cid=diamondreview. I'd much rather get this one than the one you are looking at... (note: I represent a competitor of both ED and the stores you have been to - I have absolutely no horse in the race!).
This response is so elaborate, it leaves nothing more to be said. Thanks for the detailed response @davidelevi