need help analysing this BJT circuit
My first assumption is that the intention is for the BJT to be operating in forward active mode (linear response), not saturated mode. More on that later. You cannot thevenize R1 &amp; R2 because the lower end of R2 does not connect to an ac (small signal) ground; nor do you need to thevenize in order to calculate Vce. 

No, you do not need two loops for KVL. 

Find Vce by straightforward one-loop KVL:

Vce = Vcc - R1*I1 - R3*Ie

But since I1 = Ic + Ib = Ie, 

Vce = Vcc - Ie(R1 - R3) . . . . or . . . .

Vce = Vcc - Ib(1+hFE)(R1 - R3) . . . . or . . . .

Vce = Vcc - (Ib + Ic)(R1 - R3).

Alternatively, Vce = Vcb - Vbe = R2*Ib - 0.7V; and you can make substitutions here as I did above for Ib, it depends on which current you want to solve for.

To get any more specific, we would require more data such as real resistor values in Ohms. 

PROBLEM: This is a typical textbook example for pedagogical purposes and to that extent it is not bad. But for the real world, This is not a good practical reliable circuit for forward active (linear) mode and is discouraged because it is WAY too hFE dependent which can change over time and easily change the operating point so far that you either get clipping (partial saturation depending on input signal level), or even worse, total saturation mode. And if I remember correctly, for a typical small signal amp anyway, R2 would need to be quite large (hundreds of Kohms or Mohms ?) in order to set the base current at a reasonable value for linear operation. This makes for a higher noise design. I once worked on a 1970's instrument amp that, to my horror, had this problem, and no, it was not part of the distortion circuitry; even the intended linear amp stages were like this! Amazing what they got away with long ago. It worked for years, then drifted until its operating point changed so much it was out of commission (as in no output; no sound out of the speaker, because this stage was just sitting there saturated). I redesigned it and it worked great. To fix this problem, add another resistor from the base of the BJT to ground that biases the input at a reasonable value. And make these two input bias resistors in the units of Kohms or even hundreds of ohms (if battery power is not an issue) for lower noise. It will be much more reliable.

. . . . Of course, nowadays it's mostly or entirely done with op amps . . . . . . 

Another thing this textbook example doesn't show is signal input and output nodes. It is assumed input signal drives the base of the BJT. Output can either be taken off of the collector or the emitter, It all depends on things like what kind of output impedance (CE -> high, CC -> low) and voltage gain you want. I believe I've seen some apps where output is taken off of BOTH the collector AND the emitter (for different purposes). 

Some very good references here:

MIT course notes

Illinois course notes

USC course notes

Harvard course notes