Yashin,
I'm going to guess at your first question, you didn't get the same readings for resistance as are in the manual, right?
Different meters give different readings. That is odd, they are supposed to "Measure" either resistance or voltage, right? Well meters with separate ranges can be fooled if the resistance/voltage is over the range, also these meters will not be accurate at the low end of the range. Say if you are measuring 220 ohms on a 200,000 ohm range you will get a bad reading.
A search would answer your second question about heat. The amps do get hot. Both the tubes and the transformer are designed to work at higher temperatures than any Solid State amp. The transformer gets hotter than some other tube amps.
Often the tubes don't glow enough to be seen without either getting next to them or turning off lights. What matters is if it gets warm. That is easy to check. If it is warm, it is heating. Notice I didn't say working, that requires more.
So...
1) if your measurements are not within plus or minus 15% of the manual post only the out of spec measurements, what it should be and where it was measured.
3) that is probably normal
3) check if the tube is warm, if so, you are fine, if not then measure the voltage from tube pins 4 or 5 to pin 9 on the small tube. It should be about 6.3V AC. If not post back what you read.