I just began learning the language on my own using a textbook I downloaded from a classics website. I want to make sure I am on the right track and that I am properly declining nouns and adjectives. I have reason to suspect I don't yet grasp the use of the dative case in many examples and having someone go over my answers to the exercise questions to see where I go wrong and give a brief explanation of what I did wrong/what should have been done would be greatly beneficial. Is there anywhere I can go to check if my answers to worksheet questions are correct?
It is indeed good to have human help when working through a textbook. Some textbooks can have solution keys online, but most do not. If you are not attending a Latin course at a school of any kind, looking for support online is strongly recommended to keep you on the right track.
My suggestion: When you have doubts about your understanding, ask a question on this site, Latin Language Stack Exchange.
If you ask here, don't ask for solutions to your exercises or even anyone to check the correctness of your answers. Instead, ask for understanding. For example, if you have an exercise to translate puella cani pilam dat and your are not quite sure how to do it, explain what you do understand, what you are unsure of, what is your best guess at a translation, and what makes you doubt it might not be correct. Ask for understanding, not for answers. Explain what it is that you want to know or understand. This way your question is likely to be well-received and get a good answer.
Also remember to look at questions already asked at this site. There is a lot to learn by reading questions and answers here, and in some cases they might already answer the question you have in mind. But feel free to ask a new question when you feel like it. If it relates to some other question (or you textbook), please provide a reference so others can see the context.
I'm glad to hear that yet another one has found the interest to study Latin and wants to ask for help to make sure they are learning well. I, for one, am ready to help.