Do skeletons and Skeletal champions retain or lose senses

To my mind, the overriding rules here are these:

Alternate Form

The creature retains the type and subtype of its original form.

Undead Type

• No Constitution score.

You cannot have an undead that has a Constitution score, so since Alternate Form has you retain your type, you cannot gain a Constitution score. I believe this is “more specific” than the general rule that you gain the target creature’s physical ability scores when using Alternate Form.

You could argue the opposite way, however, that Alternate Form is a more specific case than the general rule that undead do not have a Constitution score. But note that this results in a living (has a Constitution score) undead (retains that type), which to me is a good enough reason to side the other way.

As for using Charisma in place of Constitution, this is a common feature for undead, but not a universal one. In some places, that privilege requires a feat (e.g. Undead Meldshaping in Magic of Incarnum). Depending on your build, I might want to tax you for it; Cha-to-everything is a fairly potent strategy as it is, and undead is a desirable type anyway. Getting to use Charisma for yet more things, and avoiding the “weakness” of the undead type’s lack of Constitution, might be problematic. But if you weren’t already pursuing a Cha-to-everything build, I’d probably give it freely.

In 3.5, Templates are always applied consecutively:

Adding More Than One Template

In theory, there’s no limit to the number of templates you can add to a creature. To add more than one template, just apply each template one at a time. Always apply inherited templates before applying acquired templates. Whenever you add multiple templates, pay attention to the creature’s type—you may add a template that makes the creature ineligible for other templates you might want to add.

(from Improving Monsters)

Pathfinder, however, occludes the templating section in its advice on monster improvement. This means that, while the developers presumably still intend templates to be applied one-at-a-time, no rule indicating that actually exists in Pathfinder. Thusly, the answer is not specified by the rules, as written.

Since simultaneous application is not possible in the general case, however¹, not disallowing simultaneous templating will lead to seriously problematic undefined behavior (though not during game sessions).

1. That is, one cannot apply two templates simultaneously while conforming to the rules for applying templates, in general. You can do it in the special case where for each step either one template does nothing or both templates agree exactly on what must be done. This is because you apply templates in a step-by-step fashion and any conflict between instructions within a template would be unresolvable within the rules-as-written. For example, a prospective burning skeletal champion loses and gains immunity to cold simultaneously, and there's no clear end-state for its immunities as a result.