ARROW-17649: [Python] Remove remaining deprecated APIs from <= 1.0.0

[AlenkaF]

No description provided.

[jorisvandenbossche]

Looking good!

[pitrou]

@github-actions crossbow submit -g python

[github-actions]

Revision: d872906

Submitted crossbow builds: ursacomputing/crossbow @ actions-b4b0556c27

Task	Status
test-conda-python-3.10
test-conda-python-3.7
test-conda-python-3.7-hdfs-2.9.2
test-conda-python-3.7-hdfs-3.2.1
test-conda-python-3.7-pandas-0.24
test-conda-python-3.7-pandas-latest
test-conda-python-3.7-spark-v3.1.2
test-conda-python-3.8
test-conda-python-3.8-hypothesis
test-conda-python-3.8-pandas-latest
test-conda-python-3.8-pandas-nightly
test-conda-python-3.8-spark-v3.2.0
test-conda-python-3.9
test-conda-python-3.9-dask-latest
test-conda-python-3.9-dask-master
test-conda-python-3.9-pandas-master
test-conda-python-3.9-spark-master
test-debian-11-python-3
test-fedora-35-python-3
test-ubuntu-20.04-python-3

[ursabot]

Benchmark runs are scheduled for baseline = 6bf9a54 and contender = 44058ff. 44058ff is a master commit associated with this PR. Results will be available as each benchmark for each run completes.
Conbench compare runs links:
[Finished ⬇️0.0% ⬆️0.0%] ec2-t3-xlarge-us-east-2
[Failed ⬇️0.0% ⬆️0.0%] test-mac-arm
[Failed ⬇️0.0% ⬆️0.0%] ursa-i9-9960x
[Finished ⬇️0.11% ⬆️0.0%] ursa-thinkcentre-m75q
Buildkite builds:
[Finished] 44058ffd ec2-t3-xlarge-us-east-2
[Failed] 44058ffd test-mac-arm
[Failed] 44058ffd ursa-i9-9960x
[Finished] 44058ffd ursa-thinkcentre-m75q
[Finished] 6bf9a546 ec2-t3-xlarge-us-east-2
[Failed] 6bf9a546 test-mac-arm
[Failed] 6bf9a546 ursa-i9-9960x
[Finished] 6bf9a546 ursa-thinkcentre-m75q
Supported benchmarks:
ec2-t3-xlarge-us-east-2: Supported benchmark langs: Python, R. Runs only benchmarks with cloud = True
test-mac-arm: Supported benchmark langs: C++, Python, R
ursa-i9-9960x: Supported benchmark langs: Python, R, JavaScript
ursa-thinkcentre-m75q: Supported benchmark langs: C++, Java