Search are not case sensetive.
It doesn't need to match the whole tag, it just searches sequence of characters in the left field of the table.
Space is useful as begining/end of the tag.
various search fields are get combinied with logical AND.

A - any vertex.
 4 - quadrangle (example where space is useful), 4i - has incircle.
(4) - cyclic quadrilateral, (6) , etc. , n, (n) - for var number of vertex. Triangles by default, no tag. (4)i - also has incircle.
I - incenter or excenter. (AI - bisector)
O, H, G - circumcenter, othocenter, centroid. H(AAI) - orthocenter of AAI.
W, W' - midpoints of the arcs (W is on AI, WW' - diameter) (AW' - external bisector).
M - midpoint of AA
D - any point on AA
T - foot of the altitude, i.e. AH-D. Note that altitude is always AH, bisector - AI, diameter - AO, not AT, AL, AW, AA', etc...)
L - foot of bisector.
Q - any point on circumcircle. -|AQH - que-point (preferred over ()AH.-Q , MH-Q or others), -|AQI - Sharky devil point (the same), W'I-Q - mixtileniar point (the same). 
Y - any point on the incircle/excircle (may also be on not the main triangle incircle).
J - contact point of incircle or excircle. May also be of not the main triangle.
A' - diamertically opposite of A, i.e. AO-Q
P - any non-special point.
() - means circle. ()AAH for instance. ()I.A - circle through I with center A. ()AH. - circle with diameter AH (prefered over ()ATT ). (o), (i) - circumcircle, incircle, excircle. (9) - euler circle, (mx) - mixtilinear incircle. O()ADD - circumcenter of ADD.
-- means line. --HDD - line through orthocenter that intersect sides. A%--_2x - intersection of tangents.
? - what to prove. ?-- - collinearity, ?() - conciclicity, ?x - concurrency. (I prefer ?-- over ?x when it's natural).
_2 , _3 ... - several. Say JJ-D_2 , QA_2v (v means from common point) 
X - intersection of diagonals or sides of quadrangle. x also can mean intersection. Say ()AAX_4x - Miquel Point (preferred notation) , JJ-x-MM , ()_2x - two intersecting circles (when there isn't logical main triangle), 4x - compleate quadrilateral.
-| - perpendicular. H--|AM - Humpty point, O--|sm - Dumpty point. (or is it the opposite? always confuse them).
\\ - parallel. \\\\ - parallelogram, \\4 - trapezoid.
% - tangent. A%--_2x - intersection of two tangents at vertex to circumcircle.
K() - midpoint of segment. Say, K(AT) - midpoint of the altitude. ?KK - prove that two segments has common midpoint (equal segments on the same line).
X5 - NPC, X6 - simmedian point, X7 - Gergonne, X8 - Naggel, etc... (type with space before and after, inside expression they labeled just as P)
^ - angle. =^ - equal angles, ()^A%(o) - curvilinear incircle.
/\ - isoscales triangle (enclosed is spases) or just two equal segments with common vertex, (preferred over intersection of perpendicular bisector with something). /\ADDA - chain of equal segments.
.|. - reflection. A.|.AA for example.
P-P-P - reflection over point. Say, I-M-P . 
: means $\in$. P:AI - some point on angle bisector.
isg , isgP - isogonal lines, isogonal conjugate points.
/ - some relation. ?/12 , /^
bs^ - angle bisector
sq - square, -|\\ - rectangle, /\\\ - rhombus.
)( - conic. )(H - rectangular circumhyperbola.
oo% - common tangent (looking to change on )%( though).

I probably forget something and it would more obvious to just try and mess around and see what's what. 
Also note, that it's not set in stone, any of these notations may change in the future.