You have asked some questions, and I will answer them herewith. The first question is, "When making arati offerings, is it proper to meditate on the different parts of the Lord's Body?" The answer is that there is no need to meditate in that way. The Lord is actually there with you, and you are seeing all of His parts of the Body, so there is no need to meditate in that way. In regard to the other questions, food should be offered before arati. In the morning, after arati, you can offer some food and then perform kirtana.
Regarding your question about the disciplic succession coming down from Arjuna, it is just like I have got my disciples, so in the future these many disciples may have many branches of disciplic succession. So in one line of disciples we may not see another name coming from a different line. But this does not mean that person whose name does not appear was not in the disciplic succession. Narada was the Spiritual Master of Vyasadeva, and Arjuna was Vyasadeva's disciple, not as initiated disciple but there was some blood relation between them. So there is connection in this way, and it is not possible to list all such relationships in the short description given in Bhagavad-gita As It Is. Another point is that disciplic succession does not mean one has to be directly a disciple of a particular person. The conclusions which we have tried to explain in our Bhagavad-gita As It Is is the same as those conclusions of Arjuna. Arjuna accepted Krishna as the Supreme Personality of Godhead, and we also accept the same truth under the disciplic succession of Caitanya Mahaprabhu. Things equal to the same thing are equal to one another. This is an axiomatic truth. So there is no difference of opinion of understanding Krishna between ourselves and Arjuna. Another example is that a tree has many branches, and you will find one leaf here and another leaf there. But if you take this leaf and the other leaf and you press them both, you will see that the taste is the same. The taste is the conclusion, and from the taste you can understand that both leaves are from the same tree.
Regarding the problem with your father, it is not good to fight with one's father, but if he is not going to give you the money, it may be necessary to take legal steps. Since the money is to be used in Krishna's service, you should try to get it.
I have heard from Syama Dasi that she has infected her finger, and I will be glad to know of the particulars so I may give her advice in this matter. I hope this will meet you in good health.