Spoiler:
Feat 1 and Feat 2

Watch feat 2 frame by frame here

Basically?

Titan caught the meteor its carrying in the backstory and Lunafreya temporarily calls upon all the Royal Arms Noctis has yet to gather to empower him to fight Leviathan.

This includes a Royal Arm that's stuck in Niflheim across an ocean

So, scaling

First?

Let's establish the in game scale is garbage (namely the distance counter informing us the map is no more than maybe 10-15 miles across) by noting Kingsglaive informs us a strip of land south of Insomnia is at least 20 miles long (have some images). This location is demonstrated to be within an area that can still see the walls of Insomnia (compare them) and demonstrates that distance is covered in an area that has yet to cross the bridge to the greater continent under Lucis' control.

Top that off with more implicit indicators like the stupidity of developing cars that by in-game scale eat something like a tank of gas to cross 5-10 miles (I honestly forget... and no longer can test this given I have the Regalia Type-F that doesn't run out of fuel now)? And other useful indicators like an odometer that reads in both km/h and mph (will take a larger screen shot later, forgot to do that before uploading this)? And the notable fact 24 hours in game equals about 45 minutes in real life?

Pretty easy to demonstrate the distance indicator in game is purely for in-game scale and not representative of the map and landmarks.

So calc time

At a speed of ~100 km/h (in the images linked in this sentence, the odometer is circled in green), the Regalia travels from here to here in 21 seconds

Now the map

Spoiler:

Distance = 53 pixels
Meteor = 17 pixels
Lucis = 1560 pixels
Meteor/Distance = 0.321
Lucis/Distance = 29.434

Travel Time = 21 Seconds
Minute IRL = 60 seconds

Travel Time/Minute IRL = 0.35

Day In-Game = 45 minutes
Day IRL = 1,440 minutes

Day In-Game/Day IRL = 0.03125

0.03125 is what an in-game minute is equal to in actual minutes.

(Day In-Game/Day IRL)/(Travel Time/Minute IRL) = 11.2

So that stretch of road is covered over the course of 11.2 in-game minutes.

Car Speed = 100 km/h or 100,000 m/h

Minutes in Hour = 60
11.2/60 = 0.187

Distance = 18,700 meters

Meteor = 6002.7 meters

Volume = (4/3)PIr^3
r = Meteor/2

Meteor Volume = 113,250,085,600 m^3
Rock Density = 3,000 kg/m^3
Meteor Mass = 339,750,256,900,000 kilograms

Given the size of the meteor, even if I had scaled it using the in-game models and not using it's function as a natural landmark on the map?

I feel pretty confident using reentry meteor velocities typical of meteors for this backstory feat

Meteor Speed (Low End) = 11,000 m/s
Meteor Speed (High End) = 17,000 m/s

KE = 0.5mv^2

Titan's Physical Power/Durability (Low End) = 20,554,890,550,000,000,000,000 joules or 4.913 teratons
Titan's Physical Power/Durability (High End) = 49,093,912,120,000,000,000,000 joules or 11.734 teratons

And Noctis can block and parry the thing's strikes (here, here, and here). Gladio himself can temporarily block a strike before getting overpowered here. Also, the Blizzara spell is powerful enough to harm Titan to the extent Noctis' final strike destroys one of the arms that previously caught that meteor.

Lucis = 550,415.8 meters

And the speed feat?

Spoiler:

Lucis = 815 pixels
Distance = 1355 pixels
Distance/Lucis = 1.663

Distance = 915,341.475 meters

Time Frame (High End) = 5 seconds (here to here)
Time Frame (Low End) = 10.33 seconds (here to here)

Speed of Royal Arms (High End) = 183,068.295 m/s or mach 537.977
Speed of Royal Arms (Low End) = 88,610.017 m/s or mach 260.396

And Noctis fires these same Royal Arms at Leviathan the entire fight and both Leviathan and Noctis demonstrate parity to their speed with their own movements (roughly demonstrated here).