Question: When Palpatine sees the hologram of the pirate leader with Dooku, he says that a hologram can be faked, but then he believes the pirate when he sees Dooku's lightsaber. If he thinks that the pirate could have faked the hologram of Dooku, wouldn't it also be reasonable to accuse him of faking the hologram of the lightsaber?
Answer: It is to note that Count Dooku's lightsabers have a very characteristic curve handle. If you wouldn't know what this particular item looked like, you would have a hard time faking it. The sight of Dooku's lightsaber, therefore, had to convince the Jedi about the veracity of the pirate's claims.
Answer: I guess that 1) the King assumed that Ventress' droids were meant to capture the Jedi, not kill him outright. When she yells at OOM-224 to shoot Yoda, she evidently failed that expectation. 2) Sending out a bunch of Droidekas after it is plain that Master Yoda has clearly won is not a sign of good sportsmanship, either.