A good introduction is John Hayes' A Manual of Sumerian Grammar and Texts. It introduces you to the Sumerian language from the very basics and presents real texts in cuneiform from the very start with translation and ample commentary. It also contains little sections on cultural topics, material culture, religion etc. Even if it is an introduction, it can sometimes be a tad heavy on the vocabulary and may presuppose some knowledge of linguistics or grammatical terminology, but if that doesn't scare you, I'd heartily recommend it for self-study.
It contains an introductory overview of core points of grammar and history, 30 Sumerian lessons of about 20 pages each, each based on a reproduced original text and finally 7 appendices. It doesn't contain exercises per se, but you can work at translating the texts provided before you read the translation and explanation. Also, most chapters have an extra text at the end where you can practice some of what you've learnt so far.
Make sure to get the greatly expanded and rewritten 3rd edition from 2019, which is about 200 pages longer than the 2nd edition from 2000. I bought it about a year ago and have been working through it with a friend. If the price doesn't scare you, I'd go for the hardback version. The book is at a size where the paperback seems a bit unwieldy, and I regret not having ordered the hardback myself.
There are some texts that are published in the standard way with an introduction, a summary, transliteration and translation and then include photographs or autographs of the cuneiform tablets in a "Plates" section at the end of the volume. I always find these very hard to read, but you might want to have a try.
Look for instance for a publication such as Sumerian Literary Texts in the Schøyen Collection: Volume 1: Literary Sources on Old Babylonian Religion by Christopher Metcalf. It can be acquired from Amazon at quite a price, but a PDF can be found online as well with some digging.
I’m super late to this but nfr.t-jrj is supposedly recorded as npṭry in Ugaritic as well according to the Dictionary of the Ugaritic Language in the Alphabetic Tradition. And regarding Egyptian final -t, it is preserved in Coptic as part of the initial element in some feminine proper names, no? Off the top of my I can think of ϩⲁⲑⲱⲣ and ⲛⲃ̄ⲑⲱ, where ḥw.t and nb.t must have undergone something like:
Seems like a similar process must have applied to nfr.t here.
I am a beginner student like you. The only other textbook of Akkadian where there are many exercises similar to Huehnergard, is Riemschneider's Lehrbuch Des Akkadischen. There is its English translation available on Amazon:
https://www.amazon.com/Akkadian-Grammar-Translation-Riemschneiders-Akkadischen/dp/B00C3DAXFE
Its core consists of 19 lessons in OB prose. Gammar is integrated; rules concerning noun, verb, and syntax are presented from the very first lesson, not in separate sections. Author avoids inventing Akkadian sentences; presents OB omen texts, uncomplicated grammatically, and consistent in their structure. Vocabulary is ordered according to the first appearance of the word. Below is a pdf of my work with the exercises from Riemschneider. This is just a work copy, probably with mistakes:
https://drive.google.com/file/d/11K2RQNNJxWk8\_vKOP7zW36hglCGiCLm6/view?usp=sharing
Enjoy.