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None of the things you list are character flaws. They are forms of disability. A person can suffer multiple physical and psychological disabilities and still be of stirling character. A character flaw, generally speaking, is an inclination to act in an antisocial way, to let down your obligation to your fellow human beings. 

Overcoming a disability is a medical problem. Overcoming a character flaw is a moral problem. Fiction generally concerns itself with moral problems -- with choices, and the courage required to make those choices. 

There is, however, a branch of fiction that does concern itself with technical problems of various kinds: mysteries, sci fi etc. In these, the mastery of a technical problem, like a medical problem, is at least part of the attraction of the story. In most cases, at least some moral element is usually in play. See your typical TV medical drama for the balancing of technical and moral elements in a story. 

There really is no limit to the number of technical problems a character can overcome in a story. But be aware that if their solutions are purely technical, if there is no moral element to the story at all, then it is not likely to find a very wide audience. Documentaries do this kind of thing better. 

There probably is a limit to the number of moral problem a character should be asked to overcome in a story, and it is probably one. One is generally sufficient to build a story around, and the story builds by increasing pressure on that one moral problem, the one hard choice that the character has to make. More would be an unnecessary complication. 

Notice, though, that moral problems often arise from physical or psychological disabilities. People with disabilities miss out on things that others get to do. This is isolating and can lead to resentment and misanthropy, which are character flaws. Thus the moral problem that your character has to deal with may result from the physical problem they have. 

So while there may be no practical limit to the number of technical problems that the character has to face, there may be a limit imposed by the nature of the moral problem that is at the heart of the story. 

1. More physical and psychological problems than are necessary to create the moral problem at the center of the story may be superfluous and get in the way of telling the story.  

2. If the core of the story is a moral problem, then overcoming each technical problem (be that a disability or some outside problem) should be related to the moral problem in some way. If it is not, then it becomes a chunk of documentary in the middle of your story and the reader will get board (unless they happen to be fascinated by the technical subject involved). 

Technical problem that don't inform the moral development of the story, therefore, are superfluous and should be cut. The limit is not a matter of number, but of function.