Hi @jaycee7viral, 

I just recently joined Steemit. Being new here, I was exploring around and ended up finding your contest. I really had fun solving these and hoping for more great stuff like this in the future. 

It has been a while since I enjoyed using my brain. Thanks for this contest!! Here are my solutions and explanations:

1) The Lion & Unicorn:

Answer:  Thursday

Explanation: 

The lion lies on Mondays, Tuesdays and Wednesdays and the unicorn lies on Thursdays, Fridays and Saturdays. Except Sunday, there is no common day when they both speak truth or they both lie together. This means that the Lion and Unicorn are always opposites in terms on Truth and Lies (Except Sunday). Representing this pictorially, we have the following: 

Lets consider X to be 'Today' and Y to be 'Yesterday'. The lion and unicorn say that they both lied Yesterday. However as said above, they both do not have common day for lying together (Sunday being the other case can be eliminated based on the above table), which means that when they said it, they both were contradicting each other on Day X from day Y. To put it simply, what each of them said on day X is the opposite of what they said in Day Y.The only days that meet the condition from the above picture are Wednesday and Thursday where L changes to T  for Lion and T changes to L for the Unicorn. Hence Day Y(Yesterday) is Wednesday and Day X(Today) is Thursday.

2) Murder Mystery:

Answer:  Murderer -  Mother

(Long story short: Daughter witnessed her father helping her mother to murder their son)

Explanation: 

Symbols:

• M-Mother, F-Father, D - Daughter and S - Son
• While representing pairs, first symbol denotes first description and second symbol denotes second description. For example, in Witness-Helper pair, MF would mean M is the witness and F is the Helper.

Reason:

Assumption - Age of parent>Age of child 

Lets look at the conditions in a simplified manner.

1. The witness and the helper were of opposite sex.
2. The oldest person and witness were of opposite sex. 
3. The youngest person and victim were of opposite sex.
4. The helper was older than the victim.
5. The father was the oldest.
6. The youngest was not the murderer.

Out of the six conditions, condition 5 is a solid hint, so lets start with that. We know the father was the oldest. So by condition 2, the father was not the witness and that the witness was female and can either be the mother or daughter. We have the following possible pairs.

P1: Oldest-Witness: FM, FD

We already know the witness is female. From condition 1, the helper is a male. So we have the next pair

P2:Witness-Helper: DF, DS, MF, MS

With condition 3, we know that the youngest and victim were of opposite sex and that the youngest was not the victim. We don't know who is the youngest - the son or daughter. This leads to these Youngest-Victim pairs:  SM, DF

P3: Youngest-Victim: SM, DF, SD, DS

To summarize, we have inferred the following possibilities.

P1: Oldest-Witness: FM, FD

P2: Witness-Helper: DF, DS, MF, MS

P3: Youngest-Victim: SM, DF, SD, DS

Condition 4 means that the youngest was not the helper. We know from above that the youngest was not the victim. Condition 6 states that the youngest was not the murderer too. So youngest was not the witness, helper or victim which leaves us with the only conclusion that the youngest was the witness. However we know that the witness was female.  So witness being the youngest and also female means that the Daughter was the witness and the youngest. This fact reduces the above pairs to

P1: Oldest-Witness: FD

P2: Witness-Helper: DF, DS

P3: Youngest-Victim: DF, DS

The helper can be either father or son, and the victim can be either father or son. Daughter was the witness, the victim and helper were between the son and the father. The only left out role of the murderer is for the remaining member of the family, the Mother. So Mother was the Murderer. 

I have already deduced the Murderer, but if the roles of father and son too are to be concluded, then condition 4 that says helper was older than victim implies that the father was the helper and the son was the victim.

3) Genius level puzzles:

1)  

Answer: Dec 31.

Explanation: 

Let's say Phil asked Stan for his birthday on Jan 1 of current year.

Dec 30, previous year - Stan is 32 (day before yesterday)

Dec 31, previous year - Stan turns 33

Dec 31, current year - Stan turns 34

Dec 31, next year - Stan turns 35 (which is still next year)

2) 

Answer and Explanation:

• Explanation 1: The man was a father at the church
• Explanation 2: The man married his own daughter (It is morally inappropriate but still not impossible)

3) 

Answer: 5

Explanation:

Logical: 

The apples taken from her is same as the amount I receive. Once received I have 10 more apples, but we had equal amounts before the transfer. So that means I received half of the extra apples - half of 10, that is 5 apples.

Mathematical:

Let the no.of.apples each of us have = x

She gives me n apples, her current amount   = x-n

I get n apples, my current amount = x+n

If I now have 10 apples more than her, then

 (x+n) - (x-n) = 10      

  x+n-x+n =10

  2n = 10

So n=5.

For any value of x, the above equation holds, that is to say for any amount of apples we both possess, as long as she gives 5 apples to me, I will always have 10 apples more than her.

I hope my answers were convincing. 

Looking forward to more mindgames.

Cheers!!