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We know that there was a 4 years difference between them, and Renly was also a Lord and Loras his squire, meaning he was in a position of trust and authority over Loras, but we don't know when or how it started. Was their relationship healthy? Any evidence in either direction?

Judging the health of a relationship would be opinion based. To be frank, I am not sure whether I should mark this as duplicate of this question seeing as I'll be relying on material cited there to answer most of your questions with a different spin. We only have hints of their relationship, not any explicit indicator except George's interviews.

4 years do not matter at all in the society we are discussing (Nor does it matter even in the current society as long as both persons are of age).

Renly being a lord doesn't matter either since Loras is technically also a son of a High lord and didn't owe any fealty or loyalty to the Stormlord. So one can't claim that Loras may have been politically pressured into a relationship. Loras may have sworn to obey Renly as the Knight he was squiring for but I doubt Renly would have used that vow to make Loras do things he did not want to. Renly is not that sort of man, he doesn't use force at all. He has this natural charm which commands obedience. All his interactions with his vassal lords, we see him never ordering in a gruff brisk manner. We see him suggesting things to his lords which they immediately accept as commands, we see him jesting with his lords and even soldiers, we see him conferring with them. But that doesn't mean he's indecisive. When he must, he issues direct commands like when he did for appointing Loras as commander of the Vanguard.

The concept of position of trust doesn't really exist in that society of that age. Teachers in Westeros aren't exactly supposed to avoid seeking relations with their charges.

Now that being said, Squires and their masters developing strong emotional bonds is nothing new. It is in fact one of the expected outcomes. But in cases where the age difference between a Squire and his Master is as negligible as that between Renly and Loras, things can evolve into something more than just Friendship and Camaraderie. It's only natural, if you spend most of your waking hours with a person who happens to be charming, courteous and handsome, you may end up developing feelings for them. This is exactly why Cersei did not want Tommen to squire for Ser Loras Tyrell.

“The Red Keep has had no master-at-arms since Aron Santagar was
slain,” Ser Loras said, with a hint of reproach in his voice. “His
Grace is almost nine, and eager to learn. At his age he should be a
squire. Someone has to teach him.”

Someone will, but it will not be you. “Pray, who did you squire for,
ser?” she asked sweetly. “Lord Renly, was it not?”

“I had that honor.”

“Yes, I thought as much.” Cersei had seen how tight the bonds grew
between squires and the knights they served. She did not want Tommen
growing close to Loras Tyrell. The Knight of Flowers was no sort of
man for any boy to emulate.
_{AFFC- Cersei V}

As to where and when did it start, there is no indication at all. A safe guess would be Storm's End.

Renly was devoted to Loras. Catelyn Stark unwittingly noted how close the two were.

From time to time, King Renly would feed Margaery some choice morsel
off the point of his dagger, or lean over to plant the lightest of
kisses on her cheek, but it was Ser Loras who shared most of his
jests and confidences.
_{ACOK - Catelyn II}

And also:

"You might do well to pray yourself," Catelyn added.

"For victory?"

"For wisdom."

Renly laughed. "Loras, stay and help me pray. It's been so long
I've quite forgotten how. As to the rest of you, I want every man in
place by first light, armed, armored, and horsed. We shall give
Stannis a dawn he will not soon forget."
_{ACOK - Catelyn III}

Note how Renly sent everyone away and spent the night which may have been his very last for all he knew with Loras.

Loras himself appears to be devoted to Renly as well. His reaction to his death speaks volumes.

Varys gave him a simpering smile. “You would win, my lord. Lord
Alester was indeed the first to bend the knee. Many others followed.”

“Many,” Tyrion said pointedly, “but not all?”

“Not all,” agreed the eunuch. “Not Loras Tyrell, nor Randyll Tarly,
nor Mathis Rowan. And Storm’s End itself has not yielded. Ser Cortnay
Penrose holds the castle in Renly’s name, and will not believe his
liege is dead. He demands to see the mortal remains before he opens
his gates, but it seems that Renly’s corpse has unaccountably
vanished. Carried away, most likely. A fifth of Renly’s knights
departed with Ser Loras rather than bend the knee to Stannis. It’s
said the Knight of Flowers went mad when he saw his king’s body, and
slew three of Renly’s guards in his wrath, among them Emmon Cuy and
Robar Royce.”
_{ACOK- Tyrion VII}

And lastly Loras' words describing Renly following his demise really say it all that they were in love and were happy together.

"House Tyrell continues through my brothers," Ser Loras said. "It is
not necessary for a third son to wed, or breed."

"Not necessary, but some find it pleasant. What of love?"

"When the sun has set, no candle can replace it."

"Is that from a song?" Tyrion cocked his head, smiling. "Yes, you are
seventeen, I see that now."
_{ASOS- Tyrion II}