BPM280 and NANO "power supply"

Hi!
My question can be few trivial.
I have a battery (18650, 3.7V), this battery could feed Arduino (NANO) and BPM280 sensor.
Can i connect 3.3v power supply (battery + regulator like lm317) to "3.3v pin" of Arduino and to "vcc" pin of sensor???

Could i have a problems if i use the serial port (usb) in this configuration?

Can i connect 3.3v power supply (battery + regulator like lm317) to "3.3v pin" of Arduino and to "vcc" pin of sensor???

You cannot use an LM317 as this regulator needs at least a 3V higher voltage on the input side than it has to provide on the output side.
Even if you find a regulator that converts the 3.7V of the battery to the 3.3V the sensor needs you cannot feed the Nano with it as the Nano needs 5V (at least).
You can use a step-up regulator to generate 5V from your 3.7V and provide that to the Nano. Then you can use the 3.3V pin of the Nano to feed the sensor.

Can i connect BMP280 pins to arduino pins? are there problems of compatibility???? (different logic level)

I need build a very little circuit: i trying to avoid unnecessary items...

So, do you ave an idea of how to solve?

p.s. LM317 was an example because i don't know this tipe of ic's....

Can i connect BMP280 pins to arduino pins? are there problems of compatibility???? (different logic level)

You need a level converter, the BMP280 operates at 3V3 while the Nano works at 5V.

I need build a very little circuit: i trying to avoid unnecessary items...

Then change to a 3V3 Arduino model. That would make the external circuitry simpler.
That would have the additional advantage that you don't waste power by the internal linear voltage regulators of the Nano.

You can buy 3.3V versions of some Arduino compatible microcontrollers and you can also get versions that have built in connectors for charging/powering the MCU from 18650 (Or any suitable 3.7V Lipo)

i'm working with items that was on my box, i didn't buy anything.
I know that this is'n elegant solution but it works. On TTL system, the low level is less than 0.8V and the high level is more than 2V (0.6V-3.3V on CMOS system with VDD = 5V...i don't like this.....).
There are some graph that shows different logic-levels for different frequency. There are several problems, but it's working!

Thanks for helping!