The reasons for the informal portrait more likely have little to do with his early death, since people could become ill, and sicken rapidly back then. Also, it would not do to annouce to the world he was feeble and would not last long; that was almost never done at all. It was more likely to announce he was a fit young lad, as someone else said, or for other equally valid reasons. It would have been easy for the portait painter to paint his portrait in the customary clothes, even if he was wearing informal clothing when this was painted.
As for succession issues, he was practically heir for awhile, and so were some others. It is unlikely Henry would ever have had him succeed at all, because he was illigetimate, and Henry wanted to hold out hope of a legetimate male heir. He didn't want to give up, or have to be in a embarrassing position if he made Henry the heir, then a legetimate son showed up. But in a last resort, he might have made him heir. He had flounted convention before, to achieve his ends with the succession. So why not again? As for titles, it was most likely to enable him make a good match, or because he was his only illegetimate acknowledged son, I believe. It might have had overtones of preparing for the succession, but only overtones, that's all.