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I know that every schedule produced by the Timestamp-based protocol is conflict serializable. But is vice versa is true? Means is all conflict serializable schedules produced by timestamp based protocol ?
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Any schedule produced by basic time based protocol is confluct-serialuzable (there is an equivalent serial schedule which is conflict equivalent).

Same is the case for 2PL scheme. Any schedule produced by 2PL scheme is conflict serializable.

Now coming to the actual question -- answer is no. Infact 2PL and time stamp based approach both produces a strict subset of all possible conflict serializable schedules. Also not all schedules produced by 2PL can be produced by a timestamp based approach or vice versa.

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no it is not neccessary...
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as pointed out by @miniR, it is not necessary.

Timestamp ordering protocol requires the schedule to be conflict serializable in the order of the increasing timestamps. For example,

Let TS(T1) = 10, TS(T2) = 20; If the schedule turns out to be conflict serializable in the order T2->T1, it still does not get accepted in the timestamp protocol, and T1 gets aborted and re-enters the system with a new timestamp.

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suppose, TS(T1)=10 & TS(T2)=20, then following schedule is conflict serializable.

T1 T2
  W(Q)
R(Q)  

but, this is not possible under timestamp because it violets T1-->T2 

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In this I have shared a table having all types of lock classified as serializable recoverable deadlock-free.

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