I'm answering your question step-by-step, going sequentially through your problems.
The app is complete. Though some new requests might come in. These days I am only being given work that I consider is pretty bad (like formatting HTML views).
You are considering this as bad, while it may be looked at from a different perspective. Since you've mentioned you responsibility was the front-end part, it is quite logical they may assign you to do some HTML formatting. Plus, it's a part of the developer's job to correct formatting because the app's look and feel matters a lot, I don't know whether you agree with this or not.
However, another explanation to this matter, which I think is the perspective from which you are looking at, is that since you're a fresher, they're making you do such work, which are much more 'less-challenging' for a coder of your caliber. BTW, letting you do such work doesn't mean they won't give you more important task to do. Just ask your manager for more challenging tasks. From what you described, your manager appreciates you and puts a lot of trust on your skills, so I don't think he's going to ignore your request.
My manager forwarded my name for quarterly awards, but that was declined citing that I am a fresher.
In plain view, it is definitely bad to decline to recognize and reward your efforts, but it may also be the case that it's company policy not to give too much to freshers. Although, honestly, I think it's very rude and it's not good for the growth of a fresh employee as it is quite discouraging.
At the time of yearly increments, my manager told me he gave me rating of 4/4, but it got changed to 2/4 since his higher boss has fixed that rating for anyone who has not completed a year. Compared to other fresher (friends) in other companies the hike in salary is slightly on the lower side.
Like you said, this situation always varies from company to company. It depends on a lot of things, size of the company, age of the company, experience and efficiency of the management team, financial condition of the company etc. Again, company policy is also a huge reason behind it. IMO, your manager did a very bad job overrating you if company policy is to give below ratings to employees with job life less than one year. He had unnecessarily raised your expectations - he was supposed to know better about company policies than you.
To summarize, the situation that you described may be related to company policies, which in my view is pretty much demoralizing and negative to fresh employees. Your manager treated you the ideal way, with a view to groom you into an asset for the company, which is highly appreciable. But in the process, he forgot about his superiors and failed to anticipate their decisions, which led you to confusion and is highly undesirable in a professional environment. If you feel so much demoralized that you fear it can affect your productivity and growth in the current company, then you can do either one of these things - start looking for opportunities and switch immediately, or start looking for opportunities but stay for another 3-4 months, forget about recognition and increments, gather a bit more experience, and then switch.