Answer to your first question

The short answer is no. An early Egyptian (say a native speaker of Old Egyptian around say 2200 BCE) would not almost certainly not understand the speech of the later dynasties (say 332 BCE).

How to answer this question?

There are a couple of sources of evidence that we might bring to bear on a question like this.

The most obvious source is linguistic. How similar were these languages themselves? If we can read the languages of both time periods, then we can easily form a sense of how different those two languages are. Similarly, a modern English speaker might listen to Chaucer or Beowulf to get a sense of how intelligible those things would be without deliberate study. The answer is clearly "not very". Even if you do understand the older language, it's pretty obvious that it's not at similar to the language that you speak everyday. I doubt anyone would claim that Beowulf (or even Chaucer) is immediately comprehensible to a modern English speaker. If we can't understand them automatically, it's likely that they wouldn't be able to understand us either.

The second source is direct witnesses by ancient scribes. For comparison, it's pretty common to find editions of Beowulf with parallel modern translation. The existence of such texts is a pretty dead giveaway that modern people can't read the text without help, because they don't understand the language.

Linguistic Evidence for Changes in Egyptian

This is a very big topic, but I'm going to try to summarize. For a slightly longer summary, I recommend Allen's The Egyptian Language. For a more in depth study of how Egyptian changed over time, you'll need to study the various phases separately and combine the information. That's a long bibliography, but we are working to get those sorts of resources in place at r/AncientEgyptian. Some of the weekly reading groups include texts from various times, and we have resources for studying Egyptian in different phases. There are also resources for the study of Coptic etymology, which are the terms in which questions of linguistic change in Egyptian are often framed.

For the sake of illustration here I'll use a quick example. From the Autobiography of Harkhuf, I've selected a simple sentence:

"I came from my town today"

𓇍	𓈖		𓏇𓈖	𓅓	𓊖𓏏𓏤
ỉỉ	n	[ỉ]	mỉn	m	nỉwt	[i]
come	perf.	I	today	from	town	my

The same sentence, in my own (invented) Saidic Coptic:

ⲁ	ⲓ	ⲉⲓ	ⲙ	ⲡ	ⲁ	ⲧⲓⲙⲉ	ⲙ	ⲡ	ⲟⲟⲩ
a	i	i	m̩	p	a	timɛ	m̩	p	ɔʷ
pret.	I	come	from	the	my	town	in	the	day

If you only compare the literal English translations in the bottom row, it should be pretty obvious that they are quite different. There's a lot going on with both syntax and word choice that make them different. The word order is different, the way of marking aspect/tense is different, and many of the words have changed completely. The old word for town now means "Thebes" and the new word comes from an older word that once meant "harbor". It's hard to imagine that a native speaker of one could do much more than pick out the occasional word, just as we do when reading old English, and even then they would hear the word with a different intended meaning.

The key shift is the boundary between two major linguistic phases, which Allen calls Egyptian I and Egyptian II. Before Late Egyptian, there is a great deal of consistency in syntax among Middle and Old Egyptian. Late Egyptian looks very different from those, but quite similar to all later stages of the language up to and including Coptic. In short, there's a significant watershed at the beginning of Late Egyptian, which is why I can so confidently say that two people on either side of that boundary would not have understood one another.

Scribal Witnesses

Egyptian texts that were written for long periods of time show evidence of later scribes reforming them to make them more legible. A great example is the Story of Sinuhe. There's a book with various versions of the story arranged in parallel, Koch's Die Erzählung des Sinuhe. Looking at one short passage, you can see how the various later editions show orthographic changes. The "AOS" version is the Ashmolean Ostracon of Sinuhe, and it was written much later. Fittingly, it shows the most orthographic variation. Some passages have even been modified slightly, presumably because the earlier language was no longer understood.

In just about every case where an ancient text was copied later, we see a similar phenomenon. For instance, the Maxims of Ptahhotep was also recopied over time, and we see the same struggle to understand the original in later copies.

Conclusion

From two lines of reasoning, the conclusion is the same. The language of Egyptian changed too much to remain intelligible over the entire course of its very long (4000 year) history. If you want a better sense of how it changed, and if you want join us in our etymology-nerd dream project of exploring this language, come hang out with the good people at r/AncientEgyptian. Learn some languages and ask questions.

Answer to your second question

I have no idea. I hear good things about Icelandic though.

Edit: Omitted a reference.