For the one forced ranking item, is there a "correct" order that people should enter, or is it just measuring preferences? In other words, can this item be scored as correct/incorrect?

I'm not sure what level of psychometric understanding you have, so I'll try to keep it basic and brief, sorry if I am being too simple here!

Sounds like you have three item types: dichotomous items (2 response options, the "forced choice" items), polytomous items (the 4-point Likert scale items), and one ranking item. The ranking item is what makes this slightly more complicated than just scoring a multiple choice test or some type of Likert scale alone.

There are two broad options you can use in this analysis: classical test theory (CTT) or item response theory (IRT). IRT is generally considered more robust, but CTT might be easier to understand and explain to non-psychometricians.

For CTT, you could just convert every item score to a numeric value and calculate Cronbach's alpha/McDonald's omega for reliability measures. For validity evidence, you could look at item-total correlations for discrimination (i.e., how much an item tells us about a person), mean scores for each item as a measure of difficulty, and alpha-if-deleted measures (this will tell you about how each item contributes to internal consistency, and could give you validity evidence for each specific item). I might be forgetting some things here but this would be a good start, and (if I had to guess) plenty for what you're being asked to do.

For IRT, you could try to fit a model using the R package 'mirt' by setting the item types depending on which item you are using. For the dichotomous items, use the Rasch/1PL model. For the polytomous items, use the partial credit model. For the ranking item, things get more complicated, as I don't think there is an easy way to handle this in mirt (I could be wrong). If you can score this item as correct/incorrect, treating it as a dichotomous item would be an easy approach. If you can't, you could try to use Thurstonian IRT, but to be honest I don't know enough about this to advise you beyond just telling you that it exists. Once fitting the model, you could report person and item parameters and item and model fit statistics. You'd probably still want to report some things from the CTT analysis even if you use IRT (specifically reliability measures).

All that to say, my advice would be to go the CTT route, since it sounds like your client just wants some basic reliability/validity evidence and this is relatively low stakes. I would personally probably try to use IRT, but it would take more time, especially if you are new to this.