Short answer: No.
Long answer: Introduction books often say that word-initially it was a trill and finally or before a consonant an American-style retroflex R. The trill is quite probable as so many other languages of the time, including the Germanic ones, probably trilled their Rs, but at the same time there most probably was a lot of dialectal variation - just as there is today. (That's a lot of "probably"s, but that's historical linguistics for you.) This is an academic essay arguing this position (unfortunately you need to register to view it, but it's free). There's loads of evidence pointing various ways, and this author sums up the research nicely.
So all in all I'd say you can get away with following the textbook rules.
“Drout’s Quick and Easy Old English” is available in both paper and e-book, and happens to be the Medievalists.net Book-of-the-Month selection for this month.
https://www.amazon.com/dp/B09763HRWC/ref=cm_sw_r_cp_awdb_imm_A7XTDV337ZR37GMYQJ0F
There's also this,which has been translated into many languages:
Æðelgyðe Ellendæda on Wundorlande: Alice's Adventures in Wonderland in Old English (Old English Edition) https://www.amazon.com/dp/1782011129/
Word Exchange (edited by Seamus Heaney) is side by side. It is not the complete record, but it includes 123 poems (all of the most known, excepting Beowulf) and is a good place to begin, if you do not want to commit more.
Step 1: Buy Baker’s [Introduction to Old English](https://www.amazon.com/Introduction-Old-English-Peter-Baker/dp/047065984X/ref=sr_1_2?ie=UTF8&qid=1335343986&sr=8-2).”
Step 2: Create a free account on http://www.oldenglishaerobics.net to access exercises and supplements to the above book.
Step 3: Read book, make vocab flash cards, and complete exercises.
Step 4: Start reading texts independently.
Step 4b: Buy an Old English dictionary to assist with the above.
Yes! My favorite by far is Mary Savelli’s Elementary Old English: https://www.amazon.com/Elementary-Old-English-Introduction-Language/dp/1466269537/ref=mp_s_a_1_6?dchild=1&keywords=introduction+to+old+english&qid=1627107978&sr=8-6
I tried 3 other books first, but none of them offered enough comprehensible input examples to work effectively with an Anki-centric study method, IMO. Unfortunately most OE books seem stuck in the outdated “just stare at tables and look up things in a dictionary 20,000 times until it all clicks” method. Savelli is just what I needed, though!
Here’s a post with some more detail on how I made Anki + OE work for me: https://ericsiggyscott.medium.com/when-the-inductive-method-fails-learning-very-complex-grammar-with-anki-4ea4c4174ee4
Not that I'm aware of, though it has of course been translated into Latin.
Most people who study the language aren't interested in using it in a modern context, but I've always thought it interesting to think about. Also, it isn't a reconstructed language - we have plenty of texts written in it from the time it was spoken and there are very few words we've had to reconstruct. A final nitpick is that you're comparing it to Anglish. While in some cases this is a decent comparison, I wouldn't overuse it, as it isn't the same thing as OE.
Generally, new words (neologisms) are created using the same derivational techniques used in real OE words. You can also compare German or other closely-related Germanic languages. There's a good list available on the OE discord server (link available on this reddit somewhere) for you to look at with a lot of the derivation explained and various modern books written in the language (such as "Æþelgyþe ellendæda on wundorlande") contain wordlists too. Neologisms are used by those speakers who are interested in using the language in such a way, as many Latin or Sanskrit speakers use neologisms. Providing they use the proper techniques, they should be fairly understandable to most modern speakers. Check out the OE wiki for more coining help.
I've really enjoyed Savelli's Elementary Old English. Super cheap too. Nicely scaffholded, and each lesson gives a page full of vocab to pick up for its reading and translation exercises.
Pollington's intro also gives vocab incrementally, but I had a falling out with it because the ratio of example sentences to new grammar concepts drops by an order of magnitude after lesson 3.
I use Anki to learn languages inductively, from massive numbers of sentence fragments, so Pollington was never going to work out for me. Savelli gives far, far more examples to help the vocab and grammar stick through practice.
When I took an Old English module a couple of years back we used a couple of different resources for learning the language:
First was Wordloca (good grammar guide), which if you private message me I can send you a PDF of or you can make an account and use their website online. However, this doesn't use the long vowel markers, but if you use it in tandem with the second which was...
Bruce Mitchell's Guide to Old English (available here) as a reader. He does use the long vowel markers you're looking for.
If you're getting started with the language I would recommend starting with translating 'Cynewulf and Cyneheard' before tackling Bede's account of the poet Caedmon - both of which can be found in Mitchell's book.
I think this edition by Penguin Classics is close to what you're asking for.
Here's the first two pages.
I was going to suggest this book and CD set: Complete Old English (Anglo-Saxon) with Two Audio CDs: A Teach Yourself Guide (Teach Yourself Language) but after seeing the current prices on Amazon, I'm off to shrink wrap my copy and put it somewhere safe.
I wouldn't call it the best choice for learning the technicalities but getting to hear the pronunciation helped me a great deal. I'm not an academic scholar though. I just want to be able to read Beowulf in the original Old English.