Noticed a few spidery lines in this pie plate before using in the oven, then many more appeared after use. The glazing on the outside is still solid and smooth and the lines aren’t seen from the bottom. Is the plate going to crack apart? Still safe to use?  
TL;DR: that's just surface crazing, it's probably fine, but ... Potter of 30 years experience here. What you're seeing there is called "crazing".  It happens because the glaze doesn't "fit" the underlying clay perfectly, and as a result it has hairline cracks all over the plate. This is very common with high-silica clear glazes, and pretty much universal with celedon. Those cracks were always there from when the plate was made, and you're just seeing them now because they got stuff into them (more on this below). Surface crazing is generally considered harmless, except that it can lead to other problems in foodware.  First, the crazing weakens the underlying clay, and can lead to cracking while in use.  The second problem is that liquid from food can seep into those cracks, and into the clay body if it's porous even after firing (non-vitreous).  Given the "bleed" you seem to be getting around the cracks where the plate has had pie in it, I'd be concerned about this.  Bacteria can grow in those cracks and even in the clay body during storage, making the pie plate unsanitary, particularly if then used for low-temperature pies (like key lime). So, this is a case of "use it if it's the only pie plate you have, but if you have others, switch to them". 