So, I needed to take a little more "focus" time on your scenario, so I recreated the data lists and the App to go quicker. Let's see if this helps you...responses in red below.
For your DDSiteLocation: Works fine Okay - one so far...
Items property: SortByColumns(Sites, "Title", Ascending)
Value property: Title
For your DDImmersionDepartment: No values in the dropdown
Items property: Let's change to this...
ShowColumns(Filter('Customer Immersion Department' , ID in (Filter(AddColumns('Customer Immersion Sessions', "ImmDepID", ImmersionDepartments.Id), SiteLocation1.Value=DDSiteLocation.Selected.Value).ImmDepID)), "Title")
As per my understanding of the above formula, the purple ID refers to the ID in the Department. But the Green ID refers to the ID in the Sessions list. However, there is no relation between these two IDs. Please see the image below. Yes, I missed the fact that you had no connection to the list in that way. Was clearer after I threw your scenario together into an App.

I noticed a discrepancy in your Sessions list...there is a "Sales & Service", but a "Business Sales & Service" in your Department list!
For your DDSessionDate - you already have that one. (Yes, I tested this one with dummy values in the DDdepartments and it works just fine) Okay...another good one...
DDSessionDate: SortByColumns(Filter('Customer Immersion Sessions',SiteLocation1.Value=DDSiteLocation.Selected.Value,ImmersionDepartments.Value=DDDepartment.Selected.Value).CalSessionDate,"CalSessionDate",Ascending)
For your DDSessionTime - not sure what you meant by "based on all the above values selected"
I meant that the DDSessionTime should be populated by “SessionTime” choice field from Sessions list based on the DDSitelocation,DDdepartment and the DDsessiondate selected by the user in the PowerApp.
This also should be the same formula as Sessiondate, but the formula is only working for single line of text but not for choice fields/lookups.
SortByColumns(Filter('Customer Immersion Sessions',SiteLocation1.Value=DDSiteLocation.Selected.Value,ImmersionDepartments.Value=DDDepartment.Selected.Value, CalSessionDate=DDSessionDate.Selected.Value).Session Time," Session_x0020_Time ",Ascending)
Change your formula to this:
ShowColumns(AddColumns(Filter('Customer Immersion Sessions', SiteLocation1.Value=DDSitelocation.Selected.Value && ImmersionDepartments.Value=DDDepartment.Selected.Value && CalSessionDate=DDSessionDate.Selected.Value), "SessTime", SessionTime.Value), "SessTime")
If only you could help me figure out a way to display the choice/lookup values in the dropdown of Powerapps, it would be really helpful. Thanks.