The Meaning of Ar-Rajim,(Al-Hamdu Lillah),Ar-Rabb,Al-Alamin

1.The Meaning of Ar-Rajim
Ar-Rajim means, being expelled from all types of righteousness.
It was also said that Rajim means, the person who throws or bombards things, because the devil throws doubts and evil thoughts in people's hearts. The first meaning is more popular and accurate.
2.(Al-Hamdu Lillah) (all praise and thanks be to Allah) is:
all thanks are due purely to Allah, alone, not any of the objects that are being worshipped instead of Him, nor any of His creation. These thanks are due to Allah's innumerable favors and bounties, that only He knows the amount of. Allah's bounties include creating the tools that help the creation worship Him, the physical bodies with which they are able to implement His commands, the sustenance that He provides them in this life, and the comfortable life He has granted them, without anything or anyone compelling Him to do so. Allah also warned His creation and alerted them about the means and methods with which they can earn eternal dwelling in the residence of everlasting happiness. All thanks and praise are due to Allah for these favors from beginning to end.'
3.The Meaning of Ar-Rabb, the Lord
Ar-Rabb
is the owner who has full authority over his property. Ar-Rabb, linguistically means, the master or the one who has the authority to lead. All of these meanings are correct for Allah. When it is alone, the word Rabb is used only for Allah. As for other than Allah, it can be used to say Rabb Ad-Dar, the master of such and such object. Further, it was reported that Ar-Rabb is Allah's Greatest Name
4.The Meaning of Al-`Alamin
Al-`Alamin is plural for `Alam, which encompasses everything in existence except Allah. The word `Alam is itself a plural word, having no singular form. The `Alamin are different creations that exist in the heavens and the earth, on land and at sea. Every generation of creation is called an `Alam. Al-Farra` and Abu `Ubayd said, "`Alam includes all that has a mind, the Jinns, mankind, the angels and the devils, but not the animals.'' Also, Zayd bin Aslam and Abu Muhaysin said, `Alam includes all that Allah has created with a soul.'' Further, Qatadah said about,

(The Lord of the `Alamin), "Every type of creation is an `Alam.'' Az-Zajjaj also said, "Alam encompasses everything that Allah created, in this life and in the Hereafter.'' Al-Qurtubi commented, "This is the correct meaning, that the `Alam encompasses everything that Allah created in both worlds.

5.Saying Amin:-
It is recommended to say Amin after finishing the recitation of Al-Fatihah.
Amin means,
Ist Meaning:-"O Allah! Accept our invocation.''
IInd Meaning:-At-Tirmidhi said that `Amin' means, "Do not disappoint our hope''
P.S.References....Tafsir Ibn Kathir