Why is water in the lower case - 2005 KTM 250 SX

There is a rubber seal on the top side of the shift linkage and a gasket under the case. You have to drop the lower unit to repair.

In most cases, Yes!
All depends on water levels in relation to Grade of equipment to water surface level!
If filter valve is lower than level of pool surface water level, hopefully you have isolation / shut off valves before and after equipment? If you don't then answer to your question is no.
If you do have valves and when those valves are closed, then answer to your question is yes.
Answer is also yes, if pool water level is lower than filter valve.

Each gear case has two plugs - an upper, and lower. Take both plugs out and fill from the bottom till lube starts to come out the top plug. Do not fill from the top plug as an air bubble may prevent the case from getting filled completely. Gear lube is usually sold in a squeeze bottle or there's pumps available. If it takes more than one bottle, simply switch bottles, or put your finger over the hole till you get the lower plug back in. In colder climates it's best to change the lube each fall. Inspect the drained lube (old lube) for water. Water will either settle to the bottom and come out first or the lube will have a yellowish color. If there's water present - have the seals checked/replaced before refilling. Sometimes it's simply replacing the seal around the plugs. Do not let water in the lower unit freeze, as it can crack the Aluminum casing. Smaller engines might take a pint, and larger take a quart - but have extra on hand and make sure it comes out the top hole. Also check for drip spots on the floor if stored.

Unfortunately for you, the motor is out of warranty and lower units are not supposed to be cracked under any circumstances other than striking very hard some underwater obstruction. IF water was present when the motor was put away last winter, it would have frozen, expanding in the confinement of the gear housing and causing the metal casing to CRACK. Water WILL then be able to intrude the gear casing and mix with the lube oil in the lower unit leading to a breakdown if you run it without having it replaced. Get it serviced as soon as possible or, at least, get a service estimate without using it further or you'll experience a catastrophic gear failure in the lower unit and find yourself defintely looking for a new motor.

WATER PUMP - 3.3/3.8L ENGINE
REMOVAL
Drain Cooling System. Refer to procedure in this section.
Remove accessory drive belt. Refer to procedure in this section.
Remove right front lower fender shield.
Remove water pump pulley bolts and remove pulley.
Remove water pump mounting screws Water Pump - 3.3/3.8L Engine Remove water pump.
Remove and discard O-ring seal.
Clean O-ring groove and O-ring surfaces on pump and chain case cover. Take care not to scratch or gouge sealing surface.
INSTALLATION
Install new O-ring into groove Water Pump Body
Install water pump to chain case cover. Tighten screws to 12 N·m (105 in. lbs.)
Rotate pump by hand to check for freedom of movement.
Position pulley on pump. Install screws and tighten to 30 N·m (250 in. lbs.)
Install accessory drive belt. Refer to procedure in this section.
Install right front lower fender shield.
Refill Cooling System. Refer to procedure in this section.

Till the casing toward yourself then enter the lower part of the casing into the part of the base closest to you then lower the casing. The elongaged slots at the bottom of the casing will sit over the two vertical points on both sides of the base

REMOVAL

1. Drain Cooling System.
2. Remove accessory drive belt.
3. Remove right front lower fender shield.
4. Remove water pump pulley bolts and remove pulley.
   1. Remove water pump mounting screws. Remove water pump.
   2. Remove and discard O-ring seal.
   3. Clean O-ring groove and O-ring surfaces on pump and chain case cover. Take care not to scratch or gouge sealing surface.
   INSTALLATION
   
   1. Install new O-ring into groove.
   2. Install water pump to chain case cover. Tighten screws to 12 Nm (105 inch lbs.) .
   3. Rotate pump by hand to check for freedom of movement.
   4. Position pulley on pump. Install screws and tighten to 30 Nm (250 inch lbs.) .
   5. Install accessory drive belt.
   6. Install right front lower fender shield.
   7. Refill Cooling System.

True.com if its not that old a good service guy should be able to configure something.

Here is a website where a manual for you outboard may be purchased.  Outboard Marine went out of buisness in 2000 and thus no parts of origial manufacture are support is available . Therir are secondary markets .    THe Lower case splits in half and their is a seal around the prop shiftm which is pressed in. The seal between the cases are cut o-rings which are placed and glued into place with gasket seal.
The water pump is located where the case splits a little bit higher. You must open the little port on the side and take out one of the screws to the connecting shift linkage to split the case. After splitting the case the drive shaft and water pickup tube(s) wil come out of the powwer head or the tubs may stick into the power head which is ok. Place the lower skag into a vice and remove the 4 or 5 screws to the water pump housing. Remove and replace impellor and impellor plate if available. If part(pieces) of the rubber impellor is missing flush out the tubes and the power head to remove them.   When reinstalling the lower unit use a flash light to make sure that the tubes return  to the proper place in the power head and the shift lever is resecured. If you need more assistance, just write back. I was an Outboard motor mechanic for five years about the time of your motor.