Does pionium decay in massless QCD? The bound state of ${\pi}^+ {\pi}^-$ is called Pionium.
Is Pionium an Electromagnetic bound state or a Strong Force one? then Why?
Does such a bound state last forever if one works in QCD with massless quarks?
In this paper it's mentioned that the width of pionium decay in the Non-relativistic approximation is proportional to the mass difference between charged and neural pion:
Pionium decay (equation 1.2)
 A: *

*It is an EM bound state like positronium. Its lifetime is $\tau\sim 3\cdot 10^{-15}$sec, characteristic of EM. But, strong lifetimes, think of the ρ !, are $\sim 3\cdot 10^{-15-8}$sec, as you learned in your introductory HEP course, in the systematic understanding of the PDG tables section. Turning off EM would not support this bound state.

A strong bound state would involve quarks and antiquarks bound by gluons. $f_0(500)$ goes into two neutral pions (you know why the  ρ doesn't), and--boy!--it's so short-lived that its status has been debated forever.
Your pionium would "like" to decay to $\pi^+ \pi^-$, but that needs recompense for their binding energy. Since  each charged pion is 5MeV heavier than the neutral pion, it has enough energy to overcome binding and  decays to a pair of neutral pions, with enough energy (and easier to study)!

*

*But, as the two masses become comparable, this advantage is lost, and, in fact, your cited reference implicitly "goes there" with (6.1) (6.6). Given the (EM) binding energy, the two-neutral-pion mode would be below threshold too.  I believe that, nowadays, people estimate such mass differences through chiral perturbation theory and EM perturbation theory.

In fact, as per the OP's bibliographical addition, the second question may be answered more definitely by dint of the conclusions of this paper:The role of resonances in chiral perturbation theory
Generally speaking, by Dashen's formula, massless quarks would dictate strictly massless pions; but quantum fluctuations  QED quantum fluctuations can give rise to some mass for the charged pion, even in the exact chiral limit, where the quarks (and the neutral pion) remain massless (equations 6.5a and 6.5b).
This can trigger the decay of the pionium.
Re: your tetraquark comments, no...  Effimov strong mesonium threshold bound states are out of the picture here, for light quarks. What makes them virtually impossible for light quarks and barely possible for heavy ones is a long story and a very different question, which you should ask precisely and avoiding decision-tree lists.
