Non Congruent Tilings - 19

Here is the latest episode in this series.



And here is a mathoverflow discussion. The answers show tilings of the plane with mutually similar right triangles of unbounded size. An old instalment of the present series had touched upon the question of tiling the plane with mutually non-congruent but similar triangles.

Question 1: Can we tile the plane with right triangles that are similar to one another but with size bounded?

Question 2: Is there any other shape of triangle, similar and non-congruent copies of it can tile the plane?
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Update - 5th may 2023:
Here is another mathoverflow discussion.

Question: Is it possible to tile the plane with triangles that are (1) mutually similar, (2) pairwise non-congruent and (3)non-right? No other constraints.

Note 1: Reg requirement 3 above: since any right triangle can be cut into 2 pieces similar to itself and non-congruent, we can start with any right triangle and grow a plane-tiling layout outwards with progressively scaled copies of itself.

Note 2: If the question has a "yes" answer, one could consider a more constrained version of the question is got by demanding the tiles to have bounded size. Even if the basic shape of the triangle is a right triangle, this constrained version could be asked.