Tracking weight over time

Yes and yes. On the web, look at "reports." On your phone, look at "progress." When entering weight, you can choose any date on the phone.

Yes and yes.

On the desktop site, go to Reports and you can see a graph of all the weight data you've reported over the last 7, 30, 60, 90, or 365 days. (There are also graphs for measurements, if you've been reporting those, as well as calories and macros logged.) Do note, the graph only inflects when new data are added - if you reported 150lb on January 1 and then didn't update again until today, the graph will look like you were 150lb exactly every single day from then until now, at which point the line will suddenly spike up or down to the newly-reported weight. It does not extrapolate a trend line. My graph looks like a weird staircase because I weigh in once every 7 days.

To add or change your data, go to My Home > Check-In, there's a link below the table to "Edit Previous Entries" where you can also add entries for any date you choose.

On the Android app, tap the hamburger menu and go to Progress to see your graphs. Tap the + in the upper-right corner to add data for any date you choose. I assume the iOS app is laid out similarly but I don't have an iPhone. (edit to add: it appears the app *does* extrapolate a trend line, or rather connects data points directly with straight lines, rather than iterating the same weight every day until it is updated, at time scales beyond one week.)