You're always seeing line breaks there because you've misplaced your <br> elements. The following:
<</link>></span><br>
\<<if $Manor is "Laboratory">><<if $Labo_book is 1>>blablabla<</if>><br>
\<<if $Labo_note is 1>><<link "Take the note">>blablabla<</link>><</if>><</if>>
Should look something like this instead:
<</link>></span>
\<<if $Manor is "Laboratory">><<if $Labo_book is 1>><br>blablabla<</if>>
\<<if $Labo_note is 1>><br><<link "Take the note">>blablabla<</link>><</if>><</if>>
Notice how I placed the <br> tags are within each of the nested <<if>> macros, leading the content.
PS: The following is v1 code:
<<script>>state.display(state.active.title)<</script>>
While it works because of compatibility shims, you really should not be using it in v2. The correct way to do that in v2 would be one of the following:
<<script>>Engine.play(State.passage)<</script>>
That said, you don't need to do that either. In the examples you've shown, you don't need it as the <<link>> macro takes a second argument which is the passage to forward the player to when activated. Thus the following two links:
<<link "Let's Start">><<set $Start to true>><<script>>state.display(state.active.title)<</script>><</link>>
<<link "Search">><<lookaround>><<script>>state.display(state.active.title)<</script>><</link>>
Would be better written as:
<<link "Let's Start" `passage()`>><<set $Start to true>><</link>>
<<link "Search" `passage()`>><<lookaround>><</link>>
I used the passage() function in the above example, instead of State.passage, as it's a bit shorter to type. They're mostly equivalent, however, so use whichever you prefer.
Finally. In cases where you might want to use logic internal to the <<link>> to determine where it sends the player, then you're probably better off using the <<goto>> macro. For example:
<<link "Do the thing!">>
<<if /* a condition */>>
<<goto "Passage A">>
<<elseif /* another condition */>>
<<goto "Passage B">>
<<else>>
<<goto "Passage C">>
<</if>>
<</link>>