No, there's no max speed limit. Please see sources below.

Your speed will still increase with every level but the general increase rate will be curbed. So you'll still be faster as a high level but not as fast as before.

Source: https://www.tibia.com/forum/?action=thread&postid=34031503#post34031503

According to the Tibia Manual it doesn't mention that once you hit a certain level it doesn't increase anymore.

MovementA character's walking speed will increase with every level. Note that this does not influence combat speed, i.e. a character will not be able to attack or defend faster if he advances in level.

Source: https://www.tibia.com/gameguides/?subtopic=manual§ion=characters#experience

Well your speed depends on floor you walking on. There are break points which every profession have the same but some of them have better spells to reach that.

A player's actual movement speed is based on the breakpoint they have reached. Increasing speed doesn't change actual movement speed if the next breakpoint hasn't been reached. For example: if a player is walking trough the depot in Thais, where the tiles have a walking speed of 100 and that player's speed is 220, then their speed beakpoint is 4 (see the table below). To move faster, they need to reach a speed of 320, so only adding 20 extra speed (from Boots of Haste) will not change their actual movement speed, because 220 + 20 is still lower than the next breakpoint of 320. If using Haste, the resulting speed value is most often a decimal number, which gets rounded. This means that if your character has a speed of 589.6 and is affected by Haste (the Tibia client will show a speed of 589) the next breakpoint would be reached, because calculations in breakpoints are rounded up if the fractional part is greater than or equal to 0.5 and rounded down if is less than 0.5.

A player's actual movement speed is based on the breakpoint they have reached. Increasing speed doesn't change actual movement speed if the next breakpoint hasn't been reached. For example: if a player is walking trough the depot in Thais, where the tiles have a walking speed of 100 and that player's speed is 220, then their speed beakpoint is 4 (see the table below). To move faster, they need to reach a speed of 320, so only adding 20 extra speed (from Boots of Haste) will not change their actual movement speed, because 220 + 20 is still lower than the next breakpoint of 320.

If using Haste, the resulting speed value is most often a decimal number, which gets rounded. This means that if your character has a speed of 589.6 and is affected by Haste (the Tibia client will show a speed of 589) the next breakpoint would be reached, because calculations in breakpoints are rounded up if the fractional part is greater than or equal to 0.5 and rounded down if is less than 0.5.

https://imgur.com/a/G9owH#cIBlrZs There you have table with different floors and speed breakpoints.

Tha is not true. Speed increases with your level. There is formula on payer's speed level:

S= 109+L where L is player's level

To this you can always add charm Adrenaline Burst and also speed food, spells and equipment:

Speed bonuses can be provided by equipment, spells, and mounts and are either permanent or temporary.

TibiaFandom - link

Speed refers to the rate at which a player moves. A player's speed depends on many factors, such as the entity's base speed, any items or effects that entity is using, and the target tile's speed. The actual movement speed of characters, however, can only be one of a few discrete values depending on the Speed Breakpoints it reaches.

More about breakpoints you can find here - Speed Breakpoints

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