how old was Samuel when the lord visit him?

Answer 1

At least 3 years old at entering in dedicated service at the temple!

Commentary:

*** it-2 pp. 850-851 Samuel ***

"A prominent prophet (Ac 3:24; 13:20), traditionally credited with the writership of the Bible books of Judges, Ruth, and part of First Samuel. (Compare 1Sa 10:25; 1Ch 29:29.) His father Elkanah was a Levite of the nonpriestly Kohathites. (1Ch 6:27, 28, 33-38) Samuel came to have three full brothers and two full sisters.—1Sa 2:21.
--Promised to the service of Jehovah as a Nazirite by his mother Hannah before conception (1Sa 1:11), Samuel was taken to the tabernacle at Shiloh upon being weaned ( PERHAPS) at the age of at least three years; compare 2Ch 31:16) and was left there in the charge of High Priest Eli. (1Sa 1:24-28) ........
***Becomes Prophet at an Early Age.
-- At night Samuel slept in “the temple of Jehovah, where the ark of God was,” and his first assignment in the morning appears to have been to open “the doors of Jehovah’s house.” (1Sa 3:3, 15) Evidently the words “where the ark of God was” apply to the tabernacle area and are not to be understood as signifying that Samuel slept in the Most Holy. As a nonpriestly Kohathite Levite he was not entitled to see the Ark or any of the other sacred furnishings inside the sanctuary. (Nu 4:17-20) The only part of the house of Jehovah to which Samuel had access was the tabernacle courtyard. Therefore, he must have opened the doors leading into the courtyard, and it must have been there that he slept. During the period that the tabernacle was permanently located at Shiloh, various structures were likely erected, and one of these could have served as Samuel’s sleeping place.
--One night, after having retired, Samuel heard a voice calling him by name. Imagining the speaker to be High Priest Eli, he ran to see him. After this occurred three times, Eli discerned that Jehovah was calling Samuel and Eli instructed him accordingly. Jehovah then made known to Samuel his judgment against Eli’s house. Fearful, Samuel did not volunteer any information concerning the word of Jehovah until requested to do so by Eli. Thus began Samuel’s prophetic work, and all Israel eventually became aware that he was indeed Jehovah’s prophet.—1Sa 3:2-21

--This "visitation" could have been between the ages of 3-5 years old!

Answer 2

possible between 7 and 12 but the bible does not say.

Answer 3

The Bible does not say.