Yes you can file a suit but it will take time. Yes they can claim but only if they are legal heirs will be entitled to receive the same

It is self acquired property of your father 

2) sister cannot claim any share during father lifetime 

3) un registered document is in admissible in evidence 

4) you have no share in property during your father lifetime . Furth er un registered document is in admissible file n evidence 

5) if your father has by registered gift deed transferred properties to your brother you and your sister have no share in such properties 

Answers to all your queries are furnished assuming that your father is alive, as on date.

PROPERTY I

Since the agreement is not registered, it has no legal sanctity. In other words, the property is still owned by your father.

(1) There's no basis/need to file a case by your sister, as it's an unregistered document.

(2)  Since it's an unregistered document and moreover your father is alive, there's no need to file a case , as the property is still in your father's name.

PROPERTY II

Your father being the owner of his self acquired property had all rights to transfer the property in your brother's name, which is legally valid.

(3)  Even if your sister files a case to stake her claim in Property II, she is unlikely to win the case, as it's her father's self acquired property and your father, during his lifetime, is/will be independent to dispose of his self acquired property in any manner he likes, including giving away/transferring the property in your elder brother's favour.

(4) Same answer (3) applies in your case also.

(5). Assuming that your father is alive, as on date, it will be your father's prerogative to take any decision regarding his self acquired properties, including selling the property on his own without any one's consent giving share to his wife and children or gift the property to anyone or all of his choice or your father can execute a WILL to convey his intention and desire as to how and whom the properties should devolve after his death by naming beneficiary/beneficiaries.

(6).  If your father agrees, since it's his self acquired properties, let all the members of his family, including your deceased brother's widowed wife and children enter into a Family Settlement Deed and resolve the issue.

1. Un-registered against by father  in 2013 in favour of brother is not valid unless it is registered. It can be challenged after demise of father.

Property 1.

1. Signing on document which is not registered  is not of any legal significance. You can challenge the document in court and you will win the case.

Property 2.

1. This property is transferred by father by registered  transfer, neither sister nor you can claim any share in it.

As long as father  is alive, property can only be divided as per the wish of father. Only after father  you can claim share with will ¼  each that too with regard to only un-registered  property.

All problems can eb solved only after father or you can convince father  divide the property in equal shares to all.

1. If your father is living, then there is no question of anyone staking a claim for a share in his property during his lifetime, nobody has any rights, including your deceased brother's widow or you or your sister.

The so called unregistered document is not valid in law.

Therefor the transfer of that property by that document is not legally valid, as per law that property still on the name of the title holder which can be seen from the original registered document and not as per the unregistered document.

2. This property No.2 was already transferred by your father in favor of your deceased brother, hence the legal heirs of your deceased brother shall be entitled to inherit that property and not you or your father.

3. The proposed suit to be filed by your sister is not maintainable in law.

She has no rights or interests ion the property No.2 nor in any property that your father holds, at least not during the lifetime of your father.

Therefore any suit seeking her share in the property proposed by your sister is not tenable in law and she would be fighting a losing legal battle.

4. The reply given in point 3 above is equally applicable to your stake too.

5. You have been thoroughly misguided. there is no partition maintainable if approached legally to this issue.

Remember that the properties are your father's self acquired property hence none of his children nor his wife are entitled to any share in the property not at least during his lifetime.

6.  Arrange a family meeting for a reconciliation of difference of opinions, if not, then let them approach court 

Property 1: The unregistered document is legally invalid. After your father's death, his estate automatically devolved equally upon all his legal heirs, your father's mother and your mother (if they survived your father), your elder brother's legal heirs, your sister and you. Your elder brother's heirs alone shall not have any exclusive and absolute right. 

Property 2: As your father had transferred it in your elder brother's name by a registered instrument, no one else can legally claim any share.

As regards the Property 1, all the other legal heirs have to file a suit against all the legal heirs of your deceased brother's family for declaration of your title and for claiming your respective shares, at the proper court through a lawyer.

All the mentioned properties are your father's self acquired properties. So unless your father gives through proper conveyance neither of you would get. You can't even claim any share in the properties as they are your father's self acquired properties.

Since your father conveyed property no.2 to your brother through registered document, you or your sister will not be able to claim any share

With regard to property no.1, you mentioned as unregistered document, but didn't mention its nature. At any rate it is your father's self acquired property, so against his wish you will not get any share