I think most SEM software should be able to handle creating latent constructs with differently scored values (e.g., items with 0-1, 0-2, 0-3, etc) and with different numbers of items.

As far as coming up with a composite manifest score: standard practice would be to create a mean score instead of a sum. Just don't equate or combine scales across different values this way (e.g., don't change a number of times a week to a agree/disagree Likert scale). There's no reason you couldn't use a sum score also, again, so long as you're not comparing this directly to a sum score for a different construct that used different rating scales.

If you are looking at latent constructs, as above, any SEM software you use will be able to produce standardized estimates, so you can compare more easily.

I will echo the comment that the SEM software should in the measurement model phase of the analysis handle the different scaling issues. It would also inform you of the appropriateness of creating a latent construct pooling across concepts as disparate as ADL and IADL, etc. In perfect candor I suspect that pooling these into a single composite will not be statistically justified.

If you are planning to avoid the measurement model phase of the analysis and move directly to the path analysis/structural equation portion of the analysis, then one way that you can avoid the implicit weighting implied by the different scale ranges is to convert all of the measures by dividing by the theoretical upper limit, thereby creating measures that all range from 0-1 with fractional values representing the mid-points of the scale. This will eliminate the implicit weighting.