In this scenario, how is it possible for players to tell the difference between rolls and static checks without abusing savescumming to investigate?
It's possible, but never done (AFAIK). Savescumming IMO should be ignored by the developer, as a character flaw not worth designing around.
It's bad design to keep a player in the dark about how their character development will affect the game. The game should (at minimum) explicitly state that adding more points to a skill will increase the likelihood of success with that skill; IMO that is enough.
I consider it just as bad a design for a single point to significantly tip the balance, as it is for having every five points do it; where the interim four are useless until the fifth. With thresholds these individual [tipping] points suddenly guarantee ever-flawless success.
As for notification of cause for failure or success... It is not impossible to include illustrative detail for action tasks. A failure can be described as pure luck, or a surprisingly easy success, just by comparing the roll to the difficulty. In Fallout, the enemies are described as 'almost dead', or "barely/severely/... injured", and they can stay that way even after several attacks; the player doesn't know. It is very telling of the design that players ONLY know what their PCs know; this is further reflected in the awareness perk, which indicates a more detail oriented character who pays attention to enemy equipment and a more precisely interpreted apparent health.
DM doesn't tell you the required roll you need, and only tells you your degree of failure/success and the outcome
As you say.
A skill roll of 6 could be described as an unexpectedly easy success, while a successful roll of 90 could be described as a difficult challenge. These descriptions could be handled any way the developer likes. They could be a line of text in a status menu (like Fallout's), or could be a PC vocal comment, "Piece of cake!", or fully animated... (PC drops the lock pick, or snaps it, as in FO3), or combinations of any.
If the DM wasn't actually rolling dice at all and planned a predetermined outcome based on your stats instead, you would have no idea he's not actually rolling the dice.
Fallout did this. There were some predetermined outcomes where necessary for the mechanics, or plot. This was used to ensure viable character paths. For instance AFAIK/IIRC, you cannot fail to pickpocket the supermutant guard at Mariposa, to get the lock combination. These are special exceptions to the rule.
*In Fallout, you cannot fail to pickpocket your companions.