[RPG] Does Feeblemind’s saving throw use the original or current intelligence of the target

Assuming you are vulnerable to 8th level spells (meaning no 9th level Globe of Invulnerability), the only way to prevent the Ability Drain effect from Feeblemind is to succeed on the Intelligence saving throw.

There are several ways to improve your Intelligence saving throws. Here is an attempt at an exhaustive list in ascending order of inconvenience according to my own humble opinion with the first item being the best or least inconvenient option and the last item being the worst or most inconvenient option.

1. Become proficient with Intelligence saving throws.

• Take the Resilient feat (PHB page 168). This feat allows you to choose an additional type of saving throw with which to become proficient. It has the additional perk of granting a +1 bonus to an ability score of your choice. If your Intelligence score is odd, choosing it will further increase your Intelligence modifier and thus your saving throw bonus by an additional +1. This can be done as early as your 4th level in any class or as late as your 19th level in any class, unless you picked Human in which case you can do this at 1st level.
• Pick Druid, Rogue, or Wizard as your starting class at 1st level.
• Pick Monk as your starting class, and get to 14th level. At 14th level, Monks get the Diamond Soul class feature which grants proficiency with all saving throws.

2. Resistance cantrip. Allows a Druid or Cleric to give a touched creature a d4 bonus on their next saving throw (max 1 minute concentration). The Magic Initiate feat can be taken to get this cantrip while playing a class other than Druid or Cleric. Also, Warlock's can get this through their Pact of the Tome expansion feature at 3rd level.

3. Paladin's Aura of Protection. At 6th level, Paladins get the ability to add their Charisma modifier to the saving throw of any ally including themselves within a certain radius which improves as they gain class levels.

4. Bard's Bardic Inspiration. Bard's can use this class feature a number of times per day equal to their Charisma modifier to give any ally within 60 feet a minimum of a d6 bonus on their next ability check or saving throw for 10 minutes.

5. Warlock's Dark One's Own Luck. Warlocks with Fiendish patrons get this class feature at 6th level which allows them to add a d10 to one ability check or saving throw of their choice per short or long rest.

6. Gain advantage on the saving throw.

• Be under the effects of the 9th-level spell Foresight. Bards, Druids, Wizards, and Warlocks have this spell on their class spell lists. It lasts for 8 hours without concentration, provides advantage on all d20 rolls, imposes disadvantage on enemy attack rolls, and prevents you from being surprised. It's basically God Mode.
• Be a gnome. Gnomes automatically gain advantage on Intelligence, Wisdom, and Charisma saving throws made to resist a spell or magical effect as a racial trait.
• Take the Mage Slayer feat (PHB page 168). You gain advantage on any saving throws against spells cast within 5 feet of you. Close range on spell-slingers quickly!
• Take the Dungeon Delver feat (PHB page 166). Take this if you suspect that Feeblemind spell traps are likely. Grants advantage on saves to resist traps.

7. Increase your Intelligence modifier.

• Use the Ability Score Improvement class feature to boost Intelligence.
• Take feats that provide an Intelligence bonus. Examples: Keen Mind, Linguist, Observant, Resilient.

Other answers have discussed ways your fellow party members can help you recover if you fail your save and are hit by Feeblemind despite your best efforts. One additional option you might explore is to speak to your DM about the Paladin's Cleansing Touch feature. At 14th level, a Paladin can use his action to end one spell on himself or a willing creature that he touches a number of times per day equal to his Charisma modifier (minimum 1). Feeblemind explicitly states that when a creature succeeds on its saving throw, the spell ends. So presumably, the Paladin's feature should be able to cure someone afflicted with Feeblemind since it is capable of arbitrarily ending spells.

RAW, no. It's not quite true to just say it's up to DM discretion - everything is, of course, but since the rules don't say that you get spell-save ESP, then by default you don't.

Also, by historical analogy to the earlier games 5e is more like (especially AD&D 1e/2e), no. The approach to spells in those was very cut and dried, they do what they do and no more, so no extraneous "tingles" or meta-knowledge or whatever. This was part of the default "Combat As War" metaphor that has largely shifted to "Combat As Sport" in later editions.

As a result doing things like faking being affected by a spell etc. were definitely a thing in AD&D and can add some entertainment and tactics besides "make your roll" to your 5e game as well.

Of course, a GM can decide that magic works however they want in their world, and take the more 3.X'ey tack that "you just know."