Is it true that if you have multiple offers for the purchase of an item you are selling, you should give priority to the person who asked first even if the second person to ask gives a better offer?
Yes, you are correct.
As long as the buyer has not agreed to sell the product to any one buyer, then he is free to sell it to whichever buyer he wishes.
Shaikh Bin Baz rahimahullah said:
“…As for as long as he [the seller] says, ‘whoever wants to buy it, then for him is the purchase. Then [the affair is that] he, until now, did not sell it to anyone [yet]”.
However, if the seller agrees to sell it to one buyer, it is not allowed for him to entertain any other offers until the first transaction has cancelled.
ابن عمر رضي الله عنهما، أن رسول الله صلى الله عليه وسلم قال: “لا يبع بعضكم على بيع بعض، ولا يخطب على خطبة أخيه إلا أن يأذن له
Ibn ‘Umar (May Allah be pleased with them) said:
The Messenger of Allah (ﷺ) said, “A person should not enter into a transaction when his [Muslim] brother has already negotiated, nor should he make a proposal of marriage when that of his brother is pending, except with the permission of the latter.
[Bukhari and Muslim]
The Scholars derive from this Hadith the following principle:
لا شراؤه على شراء أخيه
A person should not purchase what his brother has agreed to purchase [i.e. until the sale is cancelled].
[See: ‘Ilaam al-Muwaq’ieen (5/317)] and Fath Dhil Jalal wal-Ikram Sharh Bulugh al-Maram (3/585)]
And Allah Knows Best.
Faisal Ibn Abdul Qaadir Ibn Hassan