As salamu alaikum respeted Mufti saheb,
Through the grace and mercy of Allah ta’aalah, my wife gave birth to a baby boy 3 weeks ago. We had named him and shaved his hair within the 7 days. However, due to lack of finances, i had not performed the aqeeqah nor had i given the charity which was for the hair. I am now in a better position financially to carry out these duties (3 weeks later).
1) Am i sinful for delaying these acts and what niyah should i make for the aqeeqah?
2) How do I calculate the charity which I need to give out with regard to the shaven hair and who is eligible to receive it?
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
You are not sinful for delaying the Aqīqah of your child. The performance of Aqīqah is not Fardh nor Wājib, rather it is Mustahabb (preferred).
The preferred time for slaughtering the animal and shaving the head is the seventh day upon birth. If this is not possible, then the fourteenth day, twenty first day etc. The method of calculating seven days is that whichever day the child is born, perform the Aqīqah one day before. In other words, if the child is born on a Thursday, then the Aqīqah should be performed the coming Wednesday. The fourteenth day is the Wednesday after, so on and so forth. 
You may give the price of gold or silver equivalent to the weight of the hair in charity to the poor. 
And Allah Ta’āla Knows Best
Abdul Azīm bin Abdur Rahman,
Student Darul Iftaa
Checked and Approved by,
Mufti Ebrahim Desai.
 Beheshti Zewar, Part 3, Page 31: Maktabah Al-Ilm
فتاوى محمودية, ج 26, ص 417: مكتبة محمودية
مسائل رفعت قاسمي, ج 5, ص 203: حامد كتب خانه كراشي
تحفة الالمعي شرح سنن الترمذي, ج 4, ص 452: زمزم
 Aap Ke Masaail Aur Un Ka Hal, Vol. 4, Page 228:Maktebah Ludhyanwi